-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathequation_gpt_train_100_physics.jsonl
100 lines (100 loc) · 64.6 KB
/
equation_gpt_train_100_physics.jsonl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
{"completion": " The equation for Phase constant of a driven oscillation is: <equation>\\\\tan \\\\delta = \\\\frac{{b\\\\omega }}{{m\\\\left( {\\\\omega _0^2 - \\\\omega ^2 } \\\\right)}}</equation>. Here is the brief introduction of Phase constant of a driven oscillation:\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,oscillation", "prompt": "Can you explain Phase constant of a driven oscillation?"}
{"completion": " The equation for Black Body Radiation is: <equation>w(f)=\\\\frac{8\\\\pi hf^3}{c^3}\\\\frac{1}{{\\\\rm e}^{hf/kT}-1} \\\\\\\\ \\ w(\\\\lambda)=\\\\frac{8\\\\pi hc}{\\\\lambda^5}\\\\frac{1}{{\\\\rm e}^{hc/\\\\lambda kT}-1} \\\\\\\\\\ P=A\\\\sigma T^4 \\\\\\\\\\ T\\\\lambda_{\\\\rm max}=k_{\\\\rm W}</equation>. Here is the brief introduction of Black Body Radiation:\n Latex code for the Black Body Radiation. Planck\u00e2\u20ac\u2122s law for the energy distribution for the radiation of a black body is listed above. I will briefly introduce the notations in this formulation. \n \n: Stefan-Boltzmann's law for the total power density\n: Wien's law for the maximum\n\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,quantum,Black Body Radiation", "prompt": "I am interested in Black Body Radiation?"}
{"completion": " The related materials of The Compton Effect is: 1.Physics Formulary:<url>https://johanw.home.xs4all.nl/physics.pdf</url>;", "tag": "physics,quantum,Compton Effect", "prompt": "Can you help me find related materials of The Compton Effect?"}
{"completion": " The equation for Thermodynamics Nernst Law is <equation>\\\\lim_{T\\\\rightarrow0}\\\\left(\\\\frac{\\\\partial S}{\\\\partial X}\\\\right)_{T}=0</equation>. The meaning of symbol <equation>W</equation> in Thermodynamics Nernst Law is: The work done.", "tag": "physics,thermodynamics", "prompt": "What is the meaning of the symbol <equation>W</equation> in Thermodynamics Nernst Law?"}
{"completion": " The Latex Code for equation Green functions for the initial-value problemis <equation>u(x,t)=\\\\int\\\\limits_{-\\\\infty}^\\\\infty f(x')Q(x,x',t)dx'+ \\\\int\\\\limits_{-\\\\infty}^\\\\infty g(x')P(x,x',t)dx'</equation>", "tag": "physics,green functions", "prompt": "What is the latex code of equation Green functions for the initial-value problem?"}
{"completion": " The equation for The Schr\u00f6dinger Equation is <equation>-\\\\dfrac{\\\\hbar^{2}}{2m}\\\\bigtriangledown ^{2} \\\\psi +U\\\\psi=E\\\\psi = i\\\\hbar \\\\dfrac{\\\\partial \\\\psi}{\\\\partial t} \\\\\\\\\\ H=p^2/2m+U, H\\\\psi=E\\\\psi \\\\\\\\\\ \\\\psi(x,t)=\\\\left(\\\\sum+\\\\int dE\\\\right)c(E)u_E(x)\\\\exp\\\\left(-\\\\frac{iEt}{\\\\hbar}\\\\right) \\\\\\\\\\ \\\\displaystyle J=\\\\frac{\\\\hbar}{2im}(\\\\psi^*\\\\nabla\\\\psi-\\\\psi\\\\nabla\\\\psi^*) \\\\\\\\\\ \\\\displaystyle\\\\frac{\\\\partial P(x,t)}{\\\\partial t}=-\\\\nabla J(x,t)</equation>. The meaning of symbol <equation>x_{\\rm op}=i\\hbar\\nabla_p</equation> in The Schr\u00f6dinger Equation is: The position operator.", "tag": "physics,quantum", "prompt": "What does the symbol mean <equation>x_{\\rm op}=i\\hbar\\nabla_p</equation> in The Schr\u00f6dinger Equation?"}
{"completion": " The Latex Code for equation Angular frequency for a damped oscillationis <equation>\\\\omega ' = \\\\omega _0 \\\\sqrt {1 - \\\\left( {\\\\frac{b}{{2m\\\\omega _0 }}} \\\\right)^2 } = \\\\omega _0 \\\\sqrt {1 - \\\\frac{1}{{4Q^2 }}}</equation>", "tag": "physics,angular,damped oscillation,oscillation", "prompt": "Please give me some hints on equation Angular frequency for a damped oscillation?"}
{"completion": " The Latex Code for equation Mechanics Continuity Equationis <equation>I_{V} = \\\\upsilon A</equation>", "tag": "physics,mechanics,continuity equation", "prompt": "Please give me some hints on equation Mechanics Continuity Equation?"}
{"completion": " The equation for Riemannian Tensor is: <equation>R^{\\\\mu}_{v \\\\alpha \\\\beta}T^{v}=\\\\triangledown_{\\\\alpha}\\\\triangledown_{\\\\beta}T^{\\\\mu}-\\\\triangledown_{\\\\beta}\\\\triangledown_{\\\\alpha}T^{\\\\mu} \\\\\\\\\\ \\\\triangledown_{j}a^{i}=\\\\partial_{j}a^{i}+\\\\Gamma^{i}_{jk}a^{k} \\\\\\\\\\ \\\\triangledown_{j}a_{i}=\\\\partial_{j}a_{i}-\\\\Gamma^{k}_{ij}a_{k} \\\\\\\\\\ \\\\Gamma^{i}_{jk}=\\\\frac{\\\\partial^{2} \\\\bar{x}^{l}}{\\\\partial{x^{j}}\\\\partial{x^{k}}}\\\\frac{\\\\partial{x^{i}}}{\\\\partial{\\\\bar{x}^{l}}}</equation>. Here is the brief introduction of Riemannian Tensor:Latex code for the riemannian tensor. I will briefly introduce the notations in this formulation.", "tag": "physics,riemannian rensor", "prompt": "Can you give me a brief introduction to Riemannian Tensor?"}
{"completion": " The equation for Energy change in a damped oscillation is: <equation>\\\\frac{{\\\\Delta E}}{E} = - \\\\frac{b}{m}T \\\\\\\\\\ E = E_0 \\\\exp \\\\left( { - \\\\frac{b}{m}t} \\\\right) = E_0 \\\\exp \\\\left( { - \\\\frac{t}{\\\\tau }} \\\\right)</equation>. Here is the brief introduction of Energy change in a damped oscillation:\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,oscillations", "prompt": "What's the meaning of Energy change in a damped oscillation?"}
{"completion": " The Latex Code for equation Centripetal Accelerationis <equation>a=\\\\frac{v^{2}}{r}</equation>", "tag": "physics,mechanics", "prompt": "How to write equation Centripetal Acceleration?"}
{"completion": " The equation for Optics Magnification is <equation>N=-\\\\frac{b}{v} \\\\\\\\\\ N_{\\\\alpha}=-\\\\frac{\\\\alpha_{\\\\rm syst}}{\\\\alpha_{\\\\rm none}}</equation>. The meaning of symbol <equation>\\alpha_{\\rm sys}</equation> in Optics Magnification is: size of the retinal image in the optical system.", "tag": "physics,optics,magnification", "prompt": "What is the meaning of the symbol <equation>\\alpha_{\\rm sys}</equation> in Optics Magnification?"}
{"completion": " The equation for Electric Oscillations is <equation>\\\\text{Impedance} \\\\\\\\\\ Z=R+ix \\\\\\\\\\ \\\\text{Series connection} \\\\\\\\ \\ V=IZ, Z_{\\\\rm tot}=\\\\sum_i Z_i~,~~L_{\\\\rm tot}=\\\\sum_i L_i~,~~ \\\\frac{1}{C_{\\\\rm tot}}=\\\\sum_i\\\\frac{1}{C_i}~,~~Q=\\\\frac{Z_0}{R}~,~~ Z=R(1+iQ\\\\delta) \\\\\\\\\\ \\\\text{Parallel connection} \\\\\\\\\\ \\\\frac{1}{Z_{\\\\rm tot}}=\\\\sum_i\\\\frac{1}{Z_i}~,~~ \\\\frac{1}{L_{\\\\rm tot}}=\\\\sum_i\\\\frac{1}{L_i}~,~~ C_{\\\\rm tot}=\\\\sum_i C_i~,~~Q=\\\\frac{R}{Z_0}~,~~ Z=\\\\frac{R}{1+iQ\\\\delta}</equation>. The meaning of symbol <equation>\\phi</equation> in Electric Oscillations is: Phase Angle.", "tag": "physics,oscillations", "prompt": "What is the meaning of <equation>\\phi</equation> in Electric Oscillations?"}
{"completion": " The equation for Thermodynamics Statistical Basis is <equation>P=N!\\\\prod_i\\\\frac{g_i^{n_i}}{n_i!} \\\\\\\\\\ n_i=\\\\frac{N}{Z}g_i\\\\exp\\\\left(-\\\\frac{W_i}{kT}\\\\right) \\\\\\\\\\ Z=\\\\sum\\\\limits_ig_i\\\\exp(-W_i/kT) \\\\\\\\\\ Z=\\\\frac{V(2\\\\pi mkT)^{3/2}}{h^3} \\\\\\\\\\ \\\\text{Entropy in Thermodynamic Equilibrium} \\\\\\\\\\ S=\\\\frac{U}{T}+kN\\\\ln\\\\left(\\\\frac{Z}{N}\\\\right)+kN\\\\approx\\\\frac{U}{T}+k\\\\ln\\\\left(\\\\frac{Z^N}{N!}\\\\right) \\\\\\\\\\ \\\\text{Ideal gas} \\\\\\\\\\ S=kN+kN\\\\ln\\\\left(\\\\frac{V(2\\\\pi mkT)^{3/2}}{Nh^3}\\\\right)</equation>. The meaning of symbol <equation>N</equation> in Thermodynamics Statistical Basis is: number of particles.", "tag": "physics,thermodynamics", "prompt": "What does the symbol mean <equation>N</equation> in Thermodynamics Statistical Basis?"}
{"completion": " The equation for Thermodynamics Conservation of Energy is: <equation>Q=\\\\Delta U+W \\\\\\\\\\ d\\\\hspace{-1ex}\\\\rule[1.25ex]{2mm}{0.4pt} Q=dU+d\\\\hspace{-1ex}\\\\rule[1.25ex]{2mm}{0.4pt}W \\\\\\\\\\ d\\\\hspace{-1ex}\\\\rule[1.25ex]{2mm}{0.4pt}W=pdV \\\\\\\\\\ Q=\\\\Delta H+W_{\\\\rm i}+\\\\Delta E_{\\\\rm kin}+\\\\Delta E_{\\\\rm pot}</equation>. Here is the brief introduction of Thermodynamics Conservation of Energy:\n Latex code for the Thermodynamics Introduction. I will briefly introduce the notations in this formulation. \n \n: The total added heat\n: The work done\n: The difference in the internal energy\n\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,thermodynamics", "prompt": "Please give me detailed tutorial of Thermodynamics Conservation of Energy?"}
{"completion": " The equation for Mechanic Oscillations is <equation>m\\\\ddot{x}=F(t)-k\\\\dot{x}-Cx \\\\\\\\ \\ F(t)=\\\\hat{F}\\\\cos(\\\\omega t) \\\\\\\\ \\ -m\\\\omega^2 x=F-Cx-ik\\\\omega x \\\\\\\\ \\ \\\\omega_0^2=C/m \\\\\\\\ \\ x=\\\\frac{F}{m(\\\\omega_0^2-\\\\omega^2)+ik\\\\omega} \\\\\\\\ \\ \\\\dot{x}=\\\\frac{F}{i\\\\sqrt{Cm}\\\\delta+k} \\\\\\\\ \\ \\\\delta=\\\\frac{\\\\omega}{\\\\omega_0}-\\\\frac{\\\\omega_0}{\\\\omega} \\\\\\\\ \\ Z=F/\\\\dot{x} \\\\\\\\\\ Q=\\\\frac{\\\\sqrt{Cm}}{k}</equation>. The meaning of symbol <equation>|Z|</equation> in Mechanic Oscillations is: Velocity resonance frequency: The frequency with minimal .", "tag": "physics,mechanic,oscillations", "prompt": "Can you explain the symbol <equation>|Z|</equation> in Mechanic Oscillations?"}
{"completion": " The Latex Code for equation Harmonic Oscillator Quantumis <equation>H=\\\\frac{p^2}{2m}+\\\\frac{1}{2} m\\\\omega^2 x^2= \\\\frac{1}{2} \\\\hbar\\\\omega+\\\\omega A^\\\\dagger A \\\\\\\\\\ A=\\\\sqrt{\\\\mbox{$\\\\frac{1}{2}$}m\\\\omega}x+\\\\frac{ip}{\\\\sqrt{2m\\\\omega}} \\\\\\\\\\ A^\\\\dagger=\\\\sqrt{\\\\mbox{$\\\\frac{1}{2}$}m\\\\omega}x-\\\\frac{ip}{\\\\sqrt{2m\\\\omega}} \\\\\\\\\\ HAu_E=(E-\\\\hbar\\\\omega)Au_E \\\\\\\\\\ u_n=\\\\frac{1}{\\\\sqrt{n!}}\\\\left(\\\\frac{A^\\\\dagger}{\\\\sqrt{\\\\hbar}}\\\\right)^nu_0 \\\\\\\\\\ u_0=\\\\sqrt[4]{\\\\frac{m\\\\omega}{\\\\pi\\\\hbar}}\\\\exp\\\\left(-\\\\frac{m\\\\omega x^2}{2\\\\hbar}\\\\right) \\\\\\\\\\ E_n=( \\\\frac{1}{2} +n)\\\\hbar\\\\omega</equation>", "tag": "physics,quantum", "prompt": "What is the latex code of equation Harmonic Oscillator Quantum?"}
{"completion": " The Latex Code for equation Parityis <equation>{\\\\cal P}\\\\psi(x)=\\\\psi(-x) \\\\\\\\\\ \\\\psi(x)= \\\\underbrace{\\\\frac{1}{2} (\\\\psi(x)+\\\\psi(-x))}_{\\\\rm even:~\\\\hbox{$\\\\psi^+$}}+ \\\\underbrace{\\\\frac{1}{2} (\\\\psi(x)-\\\\psi(-x))}_{\\\\rm odd:~\\\\hbox{$\\\\psi^-$}} \\\\\\\\\\ \\\\psi^+= \\\\frac{1}{2} (1+{\\\\cal P})\\\\psi(x,t) \\\\\\\\\\ \\\\psi^-= \\\\frac{1}{2} (1-{\\\\cal P})\\\\psi(x,t)</equation>", "tag": "physics,quantum", "prompt": "Can you write equation Parity?"}
{"completion": " The Latex Code for equation The Tunnel Effectis <equation>\\\\psi(x)=a^{-1/2}\\\\sin(kx) \\\\\\\\\\ E_n=n^2h^2/8a^2m \\\\\\\\\\ \\\\psi_1=A{\\\\rm e}^{ikx}+B{\\\\rm e}^{-ikx} \\\\\\\\ \\ \\\\psi_2=C{\\\\rm e}^{ik'x}+D{\\\\rm e}^{-ik'x} \\\\\\\\\\ \\\\psi_3=A'{\\\\rm e}^{ikx} \\\\\\\\\\ k'^2=2m(W-W_0)/\\\\hbar^2 \\\\\\ k^2=2mW \\\\\\\\\\ T=|A'|^2/|A|^2</equation>", "tag": "physics,quantum", "prompt": "How to write equation The Tunnel Effect?"}
{"completion": " The equation for Electric Oscillations is <equation>\\\\text{Impedance} \\\\\\\\\\ Z=R+ix \\\\\\\\\\ \\\\text{Series connection} \\\\\\\\ \\ V=IZ, Z_{\\\\rm tot}=\\\\sum_i Z_i~,~~L_{\\\\rm tot}=\\\\sum_i L_i~,~~ \\\\frac{1}{C_{\\\\rm tot}}=\\\\sum_i\\\\frac{1}{C_i}~,~~Q=\\\\frac{Z_0}{R}~,~~ Z=R(1+iQ\\\\delta) \\\\\\\\\\ \\\\text{Parallel connection} \\\\\\\\\\ \\\\frac{1}{Z_{\\\\rm tot}}=\\\\sum_i\\\\frac{1}{Z_i}~,~~ \\\\frac{1}{L_{\\\\rm tot}}=\\\\sum_i\\\\frac{1}{L_i}~,~~ C_{\\\\rm tot}=\\\\sum_i C_i~,~~Q=\\\\frac{R}{Z_0}~,~~ Z=\\\\frac{R}{1+iQ\\\\delta}</equation>. The meaning of symbol <equation>R</equation> in Electric Oscillations is: Impedance of a Resistor.", "tag": "physics,oscillations", "prompt": "Can you explain the symbol <equation>R</equation> in Electric Oscillations?"}
{"completion": " The Latex Code for equation Amplitude of a driven oscillationis <equation>A = \\\\frac{{F_0 }}{{\\\\sqrt {m^2 \\\\left( {\\\\omega _0^2 - \\\\omega ^2 } \\\\right)^2 + b^2 \\\\omega ^2 } }}</equation>", "tag": "physics,amplitude,oscillation", "prompt": "How to write equation Amplitude of a driven oscillation?"}
{"completion": " The Latex Code for equation Reflection and Transmissionis <equation>r_\\\\parallel\\\\equiv\\\\left(\\\\frac{E_{0r}}{E_{0i}}\\\\right)_\\\\parallel \\\\\\\\ \\ r_\\\\perp\\\\equiv\\\\left(\\\\frac{E_{0r}}{E_{0i}}\\\\right)_\\\\perp \\\\\\\\ \\ t_\\\\parallel\\\\equiv\\\\left(\\\\frac{E_{0t}}{E_{0i}}\\\\right)_\\\\parallel \\\\\\\\ \\ t_\\\\perp\\\\equiv\\\\left(\\\\frac{E_{0t}}{E_{0i}}\\\\right)_\\\\perp</equation>", "tag": "physics,optics,reflection,transmission", "prompt": "Can you write equation Reflection and Transmission?"}
{"completion": " The Latex Code for equation Thermodynamics Ideal Mixturesis <equation>U_{\\\\rm mixture}=\\\\sum_i n_i U^0_i \\\\\\\\ \\ H_{\\\\rm mixture}=\\\\sum_i n_i H^0_i \\\\\\\\ \\ S_{\\\\rm mixture}=n\\\\sum_i x_i S^0_i+\\\\Delta S_{\\\\rm mix} \\\\\\\\\\ \\\\Delta S_{\\\\rm mix}=-nR\\\\sum\\\\limits_i x_i\\\\ln(x_i)</equation>", "tag": "physics,thermodynamics,ideal mixtures", "prompt": "What is the latex code of equation Thermodynamics Ideal Mixtures?"}
{"completion": " The Latex Code for equation Lorentz Transformation Latexis <equation>(\\\\vec{x}^{'}, t^{'}) = (\\\\vec{x}^{'}(\\\\vec{x},t), t^{'}(\\\\vec{x},t)) \\\\\\\\ \\ \\\\vec{x}^{'} = \\\\vec{x} +\\\\frac{(\\\\gamma-1)(\\\\vec{x}\\\\vec{v}) \\\\vec{v}}{|v|^{2}} - \\\\gamma \\\\vec{v}t \\\\\\\\ \\ t^{'} = \\\\frac{\\\\gamma(t-\\\\vec{x}\\\\vec{v})}{c^{2}} \\\\\\\\ \\ \\\\gamma = \\\\frac{1}{\\\\sqrt{1-\\\\frac{v^{2}}{c^{2}}}} \\\\\\\\ \\ \\\\frac{\\\\partial^{2}}{\\\\partial{x^{2}}} + \\\\frac{\\\\partial^{2}}{\\\\partial{y^{2}}} + \\\\frac{\\\\partial^{2}}{\\\\partial{z^{2}}} - \\\\frac{1}{c^{2}} \\\\frac{\\\\partial^{2}}{\\\\partial{t^{2}}} = \\\\frac{\\\\partial^{2}}{\\\\partial{{x^{'}}^{2}}} + \\\\frac{\\\\partial^{2}}{\\\\partial{{y^{'}}^{2}}} + \\\\frac{\\\\partial^{2}}{\\\\partial{{z^{'}}^{2}}} - \\\\frac{1}{c^{2}} \\\\frac{\\\\partial^{2}}{\\\\partial{{t^{'}}^{2}}}</equation>", "tag": "physics,relativity,lorentz,transformation", "prompt": "Show me the latex code of equation Lorentz Transformation Latex?"}
{"completion": " The equation for Optical System Matrix Methods is <equation>\\\\left(\\\\begin{array}{c}n_2\\\\alpha_2\\\\\\\\y_2\\\\end{array}\\\\right)=M \\\\left(\\\\begin{array}{c}n_1\\\\alpha_1\\\\\\\\y_1\\\\end{array}\\\\right) \\\\\\\\\\ {\\\\rm Tr}(M)=1</equation>. The meaning of symbol <equation>y</equation> in Optical System Matrix Methods is: the distance to the optical axis.", "tag": "physics,optics,Matrix Methods", "prompt": "What is the meaning of <equation>y</equation> in Optical System Matrix Methods?"}
{"completion": " The equation for Quantum Wave Functions is <equation>\\\\Phi(k,t)=\\\\frac{1}{\\\\sqrt{h}}\\\\int\\\\Psi(x,t){\\\\rm e}^{-ikx}dx \\\\\\\\ \\ \\\\Psi(x,t)=\\\\frac{1}{\\\\sqrt{h}}\\\\int\\\\Phi(k,t){\\\\rm e}^{ikx}dk \\\\\\\\\\ v_{\\\\rm g}=p/m \\\\\\\\\\ E=\\\\hbar\\\\omega \\\\\\\\\\ \\\\left\\\\langle f(t) \\\\right\\\\rangle=\\\\int\\\\hspace{-1.5ex}\\\\int\\\\hspace{-1.5ex}\\\\int\\\\Psi^* f\\\\Psi d^3V \\\\\\\\ \\ \\\\left\\\\langle f_p(t) \\\\right\\\\rangle=\\\\int\\\\hspace{-1.5ex}\\\\int\\\\hspace{-1.5ex}\\\\int\\\\Phi^*f\\\\Phi d^3V_p \\\\\\\\\\ \\\\left\\\\langle f(t) \\\\right\\\\rangle=\\\\left\\\\langle \\\\Phi|f|\\\\Phi \\\\right\\\\rangle \\\\\\\\\\ \\\\left\\\\langle \\\\Phi|\\\\Phi \\\\right\\\\rangle=\\\\left\\\\langle \\\\Psi|\\\\Psi \\\\right\\\\rangle=1</equation>. The meaning of symbol <equation>\\psi</equation> in Quantum Wave Functions is: Wave Function.", "tag": "physics,quantum,wave", "prompt": "What does the symbol mean <equation>\\psi</equation> in Quantum Wave Functions?"}
{"completion": " The related materials of Quantum Wave Functions is: 1.Physics Formulary:<url>https://johanw.home.xs4all.nl/physics.pdf</url>;", "tag": "physics,quantum,wave", "prompt": "Can you help me find related materials of Quantum Wave Functions?"}
{"completion": " The equation for Thermodynamics Statistical Basis is <equation>P=N!\\\\prod_i\\\\frac{g_i^{n_i}}{n_i!} \\\\\\\\\\ n_i=\\\\frac{N}{Z}g_i\\\\exp\\\\left(-\\\\frac{W_i}{kT}\\\\right) \\\\\\\\\\ Z=\\\\sum\\\\limits_ig_i\\\\exp(-W_i/kT) \\\\\\\\\\ Z=\\\\frac{V(2\\\\pi mkT)^{3/2}}{h^3} \\\\\\\\\\ \\\\text{Entropy in Thermodynamic Equilibrium} \\\\\\\\\\ S=\\\\frac{U}{T}+kN\\\\ln\\\\left(\\\\frac{Z}{N}\\\\right)+kN\\\\approx\\\\frac{U}{T}+k\\\\ln\\\\left(\\\\frac{Z^N}{N!}\\\\right) \\\\\\\\\\ \\\\text{Ideal gas} \\\\\\\\\\ S=kN+kN\\\\ln\\\\left(\\\\frac{V(2\\\\pi mkT)^{3/2}}{Nh^3}\\\\right)</equation>. The meaning of symbol <equation>P</equation> in Thermodynamics Statistical Basis is: number of possibilities.", "tag": "physics,thermodynamics", "prompt": "Can you explain the symbol <equation>P</equation> in Thermodynamics Statistical Basis?"}
{"completion": " The equation for Optics Principal Planes is <equation>h_1=n\\\\frac{m_{11}-1}{m_{12}} \\\\\\\\ \\ h_2=n\\\\frac{m_{22}-1}{m_{12}}</equation>. The meaning of symbol <equation>N</equation> in Optics Principal Planes is: nodal points.", "tag": "physics,optics,principal planes", "prompt": "What is the meaning of <equation>N</equation> in Optics Principal Planes?"}
{"completion": " The Latex Code for equation The Schr\u00f6dinger Equationis <equation>-\\\\dfrac{\\\\hbar^{2}}{2m}\\\\bigtriangledown ^{2} \\\\psi +U\\\\psi=E\\\\psi = i\\\\hbar \\\\dfrac{\\\\partial \\\\psi}{\\\\partial t} \\\\\\\\\\ H=p^2/2m+U, H\\\\psi=E\\\\psi \\\\\\\\\\ \\\\psi(x,t)=\\\\left(\\\\sum+\\\\int dE\\\\right)c(E)u_E(x)\\\\exp\\\\left(-\\\\frac{iEt}{\\\\hbar}\\\\right) \\\\\\\\\\ \\\\displaystyle J=\\\\frac{\\\\hbar}{2im}(\\\\psi^*\\\\nabla\\\\psi-\\\\psi\\\\nabla\\\\psi^*) \\\\\\\\\\ \\\\displaystyle\\\\frac{\\\\partial P(x,t)}{\\\\partial t}=-\\\\nabla J(x,t)</equation>", "tag": "physics,quantum", "prompt": "How to write equation The Schr\u00f6dinger Equation?"}
{"completion": " The equation for Thermodynamics Statistical Basis is <equation>P=N!\\\\prod_i\\\\frac{g_i^{n_i}}{n_i!} \\\\\\\\\\ n_i=\\\\frac{N}{Z}g_i\\\\exp\\\\left(-\\\\frac{W_i}{kT}\\\\right) \\\\\\\\\\ Z=\\\\sum\\\\limits_ig_i\\\\exp(-W_i/kT) \\\\\\\\\\ Z=\\\\frac{V(2\\\\pi mkT)^{3/2}}{h^3} \\\\\\\\\\ \\\\text{Entropy in Thermodynamic Equilibrium} \\\\\\\\\\ S=\\\\frac{U}{T}+kN\\\\ln\\\\left(\\\\frac{Z}{N}\\\\right)+kN\\\\approx\\\\frac{U}{T}+k\\\\ln\\\\left(\\\\frac{Z^N}{N!}\\\\right) \\\\\\\\\\ \\\\text{Ideal gas} \\\\\\\\\\ S=kN+kN\\\\ln\\\\left(\\\\frac{V(2\\\\pi mkT)^{3/2}}{Nh^3}\\\\right)</equation>. The meaning of symbol <equation>Z</equation> in Thermodynamics Statistical Basis is: State sum Z is a normalization constant.", "tag": "physics,thermodynamics", "prompt": "What does the symbol mean <equation>Z</equation> in Thermodynamics Statistical Basis?"}
{"completion": " The equation for Thermodynamics Statistical Basis is <equation>P=N!\\\\prod_i\\\\frac{g_i^{n_i}}{n_i!} \\\\\\\\\\ n_i=\\\\frac{N}{Z}g_i\\\\exp\\\\left(-\\\\frac{W_i}{kT}\\\\right) \\\\\\\\\\ Z=\\\\sum\\\\limits_ig_i\\\\exp(-W_i/kT) \\\\\\\\\\ Z=\\\\frac{V(2\\\\pi mkT)^{3/2}}{h^3} \\\\\\\\\\ \\\\text{Entropy in Thermodynamic Equilibrium} \\\\\\\\\\ S=\\\\frac{U}{T}+kN\\\\ln\\\\left(\\\\frac{Z}{N}\\\\right)+kN\\\\approx\\\\frac{U}{T}+k\\\\ln\\\\left(\\\\frac{Z^N}{N!}\\\\right) \\\\\\\\\\ \\\\text{Ideal gas} \\\\\\\\\\ S=kN+kN\\\\ln\\\\left(\\\\frac{V(2\\\\pi mkT)^{3/2}}{Nh^3}\\\\right)</equation>. The meaning of symbol <equation>N</equation> in Thermodynamics Statistical Basis is: number of particles.", "tag": "physics,thermodynamics", "prompt": "Help me find the meaning of symbol <equation>N</equation> in Thermodynamics Statistical Basis?"}
{"completion": " The equation for Thermal Heat Capacity is <equation>C_p-C_V=T\\\\left(\\\\frac{\\\\partial p}{\\\\partial T}\\\\right)_{V}\\\\cdot\\\\left(\\\\frac{\\\\partial V}{\\\\partial T}\\\\right)_{p}=-T\\\\left(\\\\frac{\\\\partial V}{\\\\partial T}\\\\right)_{p}^2\\\\left(\\\\frac{\\\\partial p}{\\\\partial V}\\\\right)_{T}\\\\geq0 \\\\\\\\\\ \\\\displaystyle C_X=T\\\\left(\\\\frac{\\\\partial S}{\\\\partial T}\\\\right)_{X} \\\\\\\\\\ \\\\displaystyle C_p=\\\\left(\\\\frac{\\\\partial H}{\\\\partial T}\\\\right)_{p} \\\\\\\\\\ \\\\displaystyle C_V=\\\\left(\\\\frac{\\\\partial U}{\\\\partial T}\\\\right)_{V} \\\\\\\\\\ C_{mp}-C_{mV}=R</equation>. The meaning of symbol <equation>\\displaystyle C_p=\\left(\\frac{\\partial H}{\\partial T}\\right)_{p}</equation> in Thermal Heat Capacity is: The specific heat at constant pressure.", "tag": "physics,thermodynamics,heat capacity", "prompt": "Help me find the meaning of symbol <equation>\\displaystyle C_p=\\left(\\frac{\\partial H}{\\partial T}\\right)_{p}</equation> in Thermal Heat Capacity?"}
{"completion": " The Latex Code for equation Quantum Wave Functionsis <equation>\\\\Phi(k,t)=\\\\frac{1}{\\\\sqrt{h}}\\\\int\\\\Psi(x,t){\\\\rm e}^{-ikx}dx \\\\\\\\ \\ \\\\Psi(x,t)=\\\\frac{1}{\\\\sqrt{h}}\\\\int\\\\Phi(k,t){\\\\rm e}^{ikx}dk \\\\\\\\\\ v_{\\\\rm g}=p/m \\\\\\\\\\ E=\\\\hbar\\\\omega \\\\\\\\\\ \\\\left\\\\langle f(t) \\\\right\\\\rangle=\\\\int\\\\hspace{-1.5ex}\\\\int\\\\hspace{-1.5ex}\\\\int\\\\Psi^* f\\\\Psi d^3V \\\\\\\\ \\ \\\\left\\\\langle f_p(t) \\\\right\\\\rangle=\\\\int\\\\hspace{-1.5ex}\\\\int\\\\hspace{-1.5ex}\\\\int\\\\Phi^*f\\\\Phi d^3V_p \\\\\\\\\\ \\\\left\\\\langle f(t) \\\\right\\\\rangle=\\\\left\\\\langle \\\\Phi|f|\\\\Phi \\\\right\\\\rangle \\\\\\\\\\ \\\\left\\\\langle \\\\Phi|\\\\Phi \\\\right\\\\rangle=\\\\left\\\\langle \\\\Psi|\\\\Psi \\\\right\\\\rangle=1</equation>", "tag": "physics,quantum,wave", "prompt": "What is the equation of Quantum Wave Functions?"}
{"completion": " The equation for Thermodynamics Conservation of Energy is <equation>Q=\\\\Delta U+W \\\\\\\\\\ d\\\\hspace{-1ex}\\\\rule[1.25ex]{2mm}{0.4pt} Q=dU+d\\\\hspace{-1ex}\\\\rule[1.25ex]{2mm}{0.4pt}W \\\\\\\\\\ d\\\\hspace{-1ex}\\\\rule[1.25ex]{2mm}{0.4pt}W=pdV \\\\\\\\\\ Q=\\\\Delta H+W_{\\\\rm i}+\\\\Delta E_{\\\\rm kin}+\\\\Delta E_{\\\\rm pot}</equation>. The meaning of symbol <equation>W</equation> in Thermodynamics Conservation of Energy is: The work done.", "tag": "physics,thermodynamics", "prompt": "What does the symbol mean <equation>W</equation> in Thermodynamics Conservation of Energy?"}
{"completion": " The equation for Wave Equation is <equation>\\\\nabla^2u-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=\\\\frac{\\\\partial^2 u}{\\\\partial x^2}+\\\\frac{\\\\partial^2 u}{\\\\partial y^2}+\\\\frac{\\\\partial^2 u}{\\\\partial z^2}-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=0 \\\\\\\\\\ v=f\\\\lambda \\\\\\\\\\ k\\\\lambda=2\\\\pi \\\\\\\\\\ \\\\omega=2\\\\pi f \\\\\\\\\\ v_{\\\\rm g}=\\\\frac{d\\\\omega}{dk}=v_{\\\\rm ph}+k\\\\frac{dv_{\\\\rm ph}}{dk}= v_{\\\\rm ph}\\\\left(1-\\\\frac{k}{n}\\\\frac{dn}{dk}\\\\right) \\\\\\\\\\ v=\\\\sqrt{\\\\kappa/\\\\varrho}</equation>. The meaning of symbol <equation>\\displaystyle v=\\sqrt{\\left(\\frac{g\\lambda}{2\\pi}+ \\frac{2\\pi\\gamma}{\\varrho\\lambda}\\right)\\tanh\\left(\\frac{2\\pi h}{\\lambda}\\right)}</equation> in Wave Equation is: Surface waves on a liquid, h is the depth of the liquid and \\gamma the surface tension..", "tag": "physics,wave", "prompt": "What is the meaning of the symbol <equation>\\displaystyle v=\\sqrt{\\left(\\frac{g\\lambda}{2\\pi}+ \\frac{2\\pi\\gamma}{\\varrho\\lambda}\\right)\\tanh\\left(\\frac{2\\pi h}{\\lambda}\\right)}</equation> in Wave Equation?"}
{"completion": " The equation for Birefringence and Dichroism is: <equation>\\\\text{NA}</equation>. Here is the brief introduction of Birefringence and Dichroism:\n is not parallel with if the polarizability of a material is not equal in all directions. There are at least three directions, the principal axes, in which they are parallel. This results in three refractive indices ???? which can be used to construct Fresnel\u00e2\u20ac\u2122s ellipsoid. In the case \n , which happens e.g. in trigonal, hexagonal and tetragonal crystals there is one optical axis in the direction of n1. Incident light rays can now be split up in two parts: the ordinary wave is linearly polarized the plane through the transmission direction and the optical axis. The extraordinary wave is linearly polarized in the plane through the transmission direction and the optical axis. Dichroism is caused by a differential absorption of the ordinary and extraordinary wave in some materials. Double images occur when the incident ray makes an angle with the optical axis: the extraordinary wave will refract, the ordinary will not.\n \n\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,optics,girefringence,dichroism", "prompt": "Please give me detailed tutorial of Birefringence and Dichroism?"}
{"completion": " The Latex Code for equation Coupled Conductors and Transformersis <equation>M_{12}=M_{21}:=M=k\\\\sqrt{L_1L_2}=\\\\frac{N_1\\\\Phi_1}{I_2}=\\\\frac{N_2\\\\Phi_2}{I_1}\\\\sim N_1N_2 \\\\\\\\\\ \\\\frac{V_1}{V_2}=\\\\frac{I_2}{I_1}=-\\\\frac{i\\\\omega M}{i\\\\omega L_2+R_{\\\\rm load}}\\\\approx-\\\\sqrt{\\\\frac{L_1}{L_2}}=-\\\\frac{N_1}{N_2} \\\\\\\\\\ \\\\Phi_{12}=M_{12}I_2 \\\\\\\\\\ \\\\Phi_{21}=M_{21}I_1</equation>", "tag": "physics,coupled,conductors,transformers", "prompt": "What is the latex code of equation Coupled Conductors and Transformers?"}
{"completion": " The equation for Mechanics Stress is: <equation>{\\\\text{Stress}} = \\\\frac{F}{A}</equation>. Here is the brief introduction of Mechanics Stress:\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,mechanics,stress", "prompt": "Please give me detailed tutorial of Mechanics Stress?"}
{"completion": " The equation for Pendulums is: <equation>T=1/f \\\\\\\\\\ T=2\\\\pi\\\\sqrt{m/C} \\\\\\\\\\ T=2\\\\pi\\\\sqrt{I/\\\\tau} \\\\\\\\\\ T=2\\\\pi\\\\sqrt{I/\\\\kappa} \\\\\\\\\\ T=2\\\\pi\\\\sqrt{l/g}</equation>. Here is the brief introduction of Pendulums:\n Latex code for Coupled conductors and transformers. I will briefly introduce the notations in this formulation. \n \n: Oscillating spring\n: Physical pendulum\n: Torsion pendulum\n: Mathematical pendulum\n\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,pendulums", "prompt": "Can you give me a brief introduction to Pendulums?"}
{"completion": " The equation for Einstein Field Equations is: <equation>G^{\\\\alpha\\\\beta}:=R^{\\\\alpha\\\\beta}-\\\\frac{1}{2}g^{\\\\alpha\\\\beta}R \\\\\\\\\\ G_{\\\\alpha\\\\beta}=\\\\frac{8\\\\pi \\\\kappa}{c^{2}}T_{\\\\alpha\\\\beta}</equation>. Here is the brief introduction of Einstein Field Equations:Latex code for the Einstein Field Equations. I will briefly introduce the notations in this formulation. ", "tag": "physics", "prompt": "I am interested in Einstein Field Equations?"}
{"completion": " The equation for Wave Equation is <equation>\\\\nabla^2u-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=\\\\frac{\\\\partial^2 u}{\\\\partial x^2}+\\\\frac{\\\\partial^2 u}{\\\\partial y^2}+\\\\frac{\\\\partial^2 u}{\\\\partial z^2}-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=0 \\\\\\\\\\ v=f\\\\lambda \\\\\\\\\\ k\\\\lambda=2\\\\pi \\\\\\\\\\ \\\\omega=2\\\\pi f \\\\\\\\\\ v_{\\\\rm g}=\\\\frac{d\\\\omega}{dk}=v_{\\\\rm ph}+k\\\\frac{dv_{\\\\rm ph}}{dk}= v_{\\\\rm ph}\\\\left(1-\\\\frac{k}{n}\\\\frac{dn}{dk}\\\\right) \\\\\\\\\\ v=\\\\sqrt{\\\\kappa/\\\\varrho}</equation>. The meaning of symbol <equation>v=\\sqrt{\\kappa/\\varrho}</equation> in Wave Equation is: Pressure waves in a liquid or gas, is the modulus of compression..", "tag": "physics,wave", "prompt": "What does the symbol mean <equation>v=\\sqrt{\\kappa/\\varrho}</equation> in Wave Equation?"}
{"completion": " The Latex Code for equation Stress-energy Tensoris <equation>T_{\\\\mu v}=(\\\\varrho c^{2}+p)u_{p}u_{v}+pg_{\\\\mu v}+\\\\frac{1}{c^{2}}(F^{\\\\mu}_{\\\\alpha}F^{\\\\alpha v} + \\\\frac{1}{4}g^{\\\\mu v}F^{\\\\alpha\\\\beta}F_{\\\\alpha\\\\beta}) \\\\\\\\\\ \\\\triangledown_{v} T_{\\\\mu v}=0 \\\\\\\\\\ F_{\\\\alpha\\\\beta}=\\\\frac{\\\\partial{A_{\\\\beta}}}{\\\\partial{x^{\\\\alpha}}} - \\\\frac{\\\\partial{A_{\\\\alpha}}}{\\\\partial{x^{\\\\beta}}} \\\\\\\\\\ \\\\frac{d p_{\\\\alpha}}{d \\\\tau}=qF_{\\\\alpha\\\\beta}u^{\\\\beta}</equation>", "tag": "physics,stress-energy tensor", "prompt": "What is the equation of Stress-energy Tensor?"}
{"completion": " The Latex Code for equation Throttle Processesis <equation>\\\\text{Isobaric Processes} \\\\\\\\\\ H_2-H_1=\\\\int_1^2 C_pdT \\\\\\\\\\ \\\\text{Reversible Isobaric Process} \\\\\\\\\\ H_2-H_1=Q_{\\\\rm rev}</equation>", "tag": "physics,thermodynamics,throttle processes", "prompt": "What is the equation of Throttle Processes?"}
{"completion": " The Latex Code for equation Einstein Field Equationsis <equation>G^{\\\\alpha\\\\beta}:=R^{\\\\alpha\\\\beta}-\\\\frac{1}{2}g^{\\\\alpha\\\\beta}R \\\\\\\\\\ G_{\\\\alpha\\\\beta}=\\\\frac{8\\\\pi \\\\kappa}{c^{2}}T_{\\\\alpha\\\\beta}</equation>", "tag": "physics", "prompt": "What is the latex code of equation Einstein Field Equations?"}
{"completion": " The equation for Pendulums is <equation>T=1/f \\\\\\\\\\ T=2\\\\pi\\\\sqrt{m/C} \\\\\\\\\\ T=2\\\\pi\\\\sqrt{I/\\\\tau} \\\\\\\\\\ T=2\\\\pi\\\\sqrt{I/\\\\kappa} \\\\\\\\\\ T=2\\\\pi\\\\sqrt{l/g}</equation>. The meaning of symbol <equation>T=2\\pi\\sqrt{I/\\tau}</equation> in Pendulums is: Physical pendulum.", "tag": "physics,pendulums", "prompt": "Can you explain the symbol <equation>T=2\\pi\\sqrt{I/\\tau}</equation> in Pendulums?"}
{"completion": " The Latex Code for equation Phase constant of a driven oscillationis <equation>\\\\tan \\\\delta = \\\\frac{{b\\\\omega }}{{m\\\\left( {\\\\omega _0^2 - \\\\omega ^2 } \\\\right)}}</equation>", "tag": "physics,oscillation", "prompt": "How to write equation Phase constant of a driven oscillation?"}
{"completion": " The equation for Thermal Heat Capacity is <equation>C_p-C_V=T\\\\left(\\\\frac{\\\\partial p}{\\\\partial T}\\\\right)_{V}\\\\cdot\\\\left(\\\\frac{\\\\partial V}{\\\\partial T}\\\\right)_{p}=-T\\\\left(\\\\frac{\\\\partial V}{\\\\partial T}\\\\right)_{p}^2\\\\left(\\\\frac{\\\\partial p}{\\\\partial V}\\\\right)_{T}\\\\geq0 \\\\\\\\\\ \\\\displaystyle C_X=T\\\\left(\\\\frac{\\\\partial S}{\\\\partial T}\\\\right)_{X} \\\\\\\\\\ \\\\displaystyle C_p=\\\\left(\\\\frac{\\\\partial H}{\\\\partial T}\\\\right)_{p} \\\\\\\\\\ \\\\displaystyle C_V=\\\\left(\\\\frac{\\\\partial U}{\\\\partial T}\\\\right)_{V} \\\\\\\\\\ C_{mp}-C_{mV}=R</equation>. The meaning of symbol <equation>\\displaystyle C_p=\\left(\\frac{\\partial H}{\\partial T}\\right)_{p}</equation> in Thermal Heat Capacity is: The specific heat at constant pressure.", "tag": "physics,thermodynamics,heat capacity", "prompt": "What is the meaning of the symbol <equation>\\displaystyle C_p=\\left(\\frac{\\partial H}{\\partial T}\\right)_{p}</equation> in Thermal Heat Capacity?"}
{"completion": " The Latex Code for equation Displacement of a slightly damped oscillatoris <equation>x = A_0 \\\\exp \\\\left( { - \\\\frac{b}{{2m}}t} \\\\right)\\\\cos \\\\left( {\\\\omega 't + \\\\delta } \\\\right)</equation>", "tag": "physics,oscillations", "prompt": "Can you write equation Displacement of a slightly damped oscillator?"}
{"completion": " The equation for Coupled Conductors and Transformers is <equation>M_{12}=M_{21}:=M=k\\\\sqrt{L_1L_2}=\\\\frac{N_1\\\\Phi_1}{I_2}=\\\\frac{N_2\\\\Phi_2}{I_1}\\\\sim N_1N_2 \\\\\\\\\\ \\\\frac{V_1}{V_2}=\\\\frac{I_2}{I_1}=-\\\\frac{i\\\\omega M}{i\\\\omega L_2+R_{\\\\rm load}}\\\\approx-\\\\sqrt{\\\\frac{L_1}{L_2}}=-\\\\frac{N_1}{N_2} \\\\\\\\\\ \\\\Phi_{12}=M_{12}I_2 \\\\\\\\\\ \\\\Phi_{21}=M_{21}I_1</equation>. The meaning of symbol <equation>k</equation> in Coupled Conductors and Transformers is: Coupling factor.", "tag": "physics,coupled,conductors,transformers", "prompt": "Help me find the meaning of symbol <equation>k</equation> in Coupled Conductors and Transformers?"}
{"completion": " The Latex Code for equation Bulk Modulusis <equation>B = - \\\\frac{P}{{\\\\Delta V}/V}</equation>", "tag": "physics,mechanics,bulk modulus", "prompt": "How to write equation Bulk Modulus?"}
{"completion": " The equation for Fabry Perot Interferometer is <equation>T+R+A=1</equation>. The meaning of symbol <equation>[1+F\\sin^2(\\theta)]^{-1}:={\\cal A}(\\theta)</equation> in Fabry Perot Interferometer is: Airy function.", "tag": "physics,optics,fabry perot", "prompt": "What is the meaning of <equation>[1+F\\sin^2(\\theta)]^{-1}:={\\cal A}(\\theta)</equation> in Fabry Perot Interferometer?"}
{"completion": " The equation for Plane Waves is <equation>u(\\\\vec{x},t)=2^n\\\\hat{u}\\\\cos(\\\\omega t)\\\\sum_{i=1}^n\\\\sin(k_ix_i) \\\\\\\\\\ u(\\\\vec{x},t)=\\\\hat{u}\\\\cos(\\\\vec{k}\\\\cdot\\\\vec{x}\\\\pm\\\\omega t+\\\\varphi) \\\\\\\\\\ \\\\frac{f}{f_0}=\\\\frac{v_{\\\\rm f}-v_{\\\\rm obs}}{v_{\\\\rm f}}</equation>. The meaning of symbol <equation>u(\\vec{x},t)</equation> in Plane Waves is: harmonic plane wave is defined as u(x,t).", "tag": "physics,plane waves", "prompt": "Can you explain the symbol <equation>u(\\vec{x},t)</equation> in Plane Waves?"}
{"completion": " The Latex Code for equation Red and Blue Shiftis <equation>\\\\vec{e_{v}}\\\\vec{e_{r}}=\\\\cos(\\\\Phi) \\\\\\\\\\ \\\\frac{f^{'}}{f}=\\\\gamma(1-\\\\frac{v\\\\cos(\\\\Phi)}{c}) \\\\\\\\\\ \\\\frac{\\\\Delta f}{f}=\\\\frac{\\\\kappa M}{rc^{2}} \\\\\\\\\\ \\\\frac{\\\\lambda_{0}}{\\\\lambda_{1}}=\\\\frac{R_{0}}{R_{1}}</equation>", "tag": "physics,red and blue shift", "prompt": "How to write equation Red and Blue Shift?"}
{"completion": " The equation for Wave Equation is <equation>\\\\nabla^2u-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=\\\\frac{\\\\partial^2 u}{\\\\partial x^2}+\\\\frac{\\\\partial^2 u}{\\\\partial y^2}+\\\\frac{\\\\partial^2 u}{\\\\partial z^2}-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=0 \\\\\\\\\\ v=f\\\\lambda \\\\\\\\\\ k\\\\lambda=2\\\\pi \\\\\\\\\\ \\\\omega=2\\\\pi f \\\\\\\\\\ v_{\\\\rm g}=\\\\frac{d\\\\omega}{dk}=v_{\\\\rm ph}+k\\\\frac{dv_{\\\\rm ph}}{dk}= v_{\\\\rm ph}\\\\left(1-\\\\frac{k}{n}\\\\frac{dn}{dk}\\\\right) \\\\\\\\\\ v=\\\\sqrt{\\\\kappa/\\\\varrho}</equation>. The meaning of symbol <equation>v=\\sqrt{\\kappa/\\varrho}</equation> in Wave Equation is: Pressure waves in a liquid or gas, is the modulus of compression..", "tag": "physics,wave", "prompt": "Help me find the meaning of symbol <equation>v=\\sqrt{\\kappa/\\varrho}</equation> in Wave Equation?"}
{"completion": " The related materials of Viscous Flow is: 1.Physics Formulary:<url>https://johanw.home.xs4all.nl/physics.pdf</url>;", "tag": "physics,mechanics,viscous flow", "prompt": "Can you help me find related materials of Viscous Flow?"}
{"completion": " The equation for Phase constant of a driven oscillation is: <equation>\\\\tan \\\\delta = \\\\frac{{b\\\\omega }}{{m\\\\left( {\\\\omega _0^2 - \\\\omega ^2 } \\\\right)}}</equation>. Here is the brief introduction of Phase constant of a driven oscillation:\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,oscillation", "prompt": "Please give me detailed tutorial of Phase constant of a driven oscillation?"}
{"completion": " The equation for Thermodynamics Definitions is <equation>f(x,y,z)=0 \\\\\\\\\\ dz=\\\\left(\\\\frac{\\\\partial z}{\\\\partial x}\\\\right)_{y}dx+\\\\left(\\\\frac{\\\\partial z}{\\\\partial y}\\\\right)_{x}dy \\\\\\\\\\ \\\\left(\\\\frac{\\\\partial x}{\\\\partial y}\\\\right)_{z}\\\\cdot\\\\left(\\\\frac{\\\\partial y}{\\\\partial z}\\\\right)_{x}\\\\cdot\\\\left(\\\\frac{\\\\partial z}{\\\\partial x}\\\\right)_{y}=-1 \\\\\\\\\\ \\\\varepsilon^m F(x,y,z)=F(\\\\varepsilon x,\\\\varepsilon y,\\\\varepsilon z) \\\\\\\\\\ mF(x,y,z)=x\\\\frac{\\\\partial F}{\\\\partial x}+y\\\\frac{\\\\partial F}{\\\\partial y}+z\\\\frac{\\\\partial F}{\\\\partial z}</equation>. The meaning of symbol <equation>\\displaystyle \\gamma_p=\\frac{1}{V}\\left(\\frac{\\partial V}{\\partial T}\\right)_{p}</equation> in Thermodynamics Definitions is: The isobaric volume coefficient.", "tag": "physics,thermodynamics", "prompt": "Help me find the meaning of symbol <equation>\\displaystyle \\gamma_p=\\frac{1}{V}\\left(\\frac{\\partial V}{\\partial T}\\right)_{p}</equation> in Thermodynamics Definitions?"}
{"completion": " The equation for Diffraction is: <equation>\\\\frac{I(\\\\theta)}{I_0}=\\\\left(\\\\frac{\\\\sin(u)}{u}\\\\right)^2\\\\cdot \\\\left(\\\\frac{\\\\sin(Nv)}{\\\\sin(v)}\\\\right)^2 \\\\\\\\\\ u=\\\\pi b\\\\sin(\\\\theta)/\\\\lambda \\\\\\\\\\ v=\\\\pi d\\\\sin(\\\\theta)/\\\\lambda</equation>. Here is the brief introduction of Diffraction:\n A light ray passing through a prism is refracted twice and aquires a deviation from its original direction.\n \n: is the number of slits\n: is the width of a slit\n: is distance between the slits\n: is the maxima in intensity\n: The diffraction through a spherical aperture with radius \\alpha\n: The diffraction pattern of a rectangular aperture at distance R with length \\alpha in the x -direction and b in the y-direction\n\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,optics,diffraction", "prompt": "Please give me detailed tutorial of Diffraction?"}
{"completion": " The equation for Riemannian Tensor is: <equation>R^{\\\\mu}_{v \\\\alpha \\\\beta}T^{v}=\\\\triangledown_{\\\\alpha}\\\\triangledown_{\\\\beta}T^{\\\\mu}-\\\\triangledown_{\\\\beta}\\\\triangledown_{\\\\alpha}T^{\\\\mu} \\\\\\\\\\ \\\\triangledown_{j}a^{i}=\\\\partial_{j}a^{i}+\\\\Gamma^{i}_{jk}a^{k} \\\\\\\\\\ \\\\triangledown_{j}a_{i}=\\\\partial_{j}a_{i}-\\\\Gamma^{k}_{ij}a_{k} \\\\\\\\\\ \\\\Gamma^{i}_{jk}=\\\\frac{\\\\partial^{2} \\\\bar{x}^{l}}{\\\\partial{x^{j}}\\\\partial{x^{k}}}\\\\frac{\\\\partial{x^{i}}}{\\\\partial{\\\\bar{x}^{l}}}</equation>. Here is the brief introduction of Riemannian Tensor:Latex code for the riemannian tensor. I will briefly introduce the notations in this formulation.", "tag": "physics,riemannian rensor", "prompt": "What's the meaning of Riemannian Tensor?"}
{"completion": " The equation for Wave Equation is <equation>\\\\nabla^2u-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=\\\\frac{\\\\partial^2 u}{\\\\partial x^2}+\\\\frac{\\\\partial^2 u}{\\\\partial y^2}+\\\\frac{\\\\partial^2 u}{\\\\partial z^2}-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=0 \\\\\\\\\\ v=f\\\\lambda \\\\\\\\\\ k\\\\lambda=2\\\\pi \\\\\\\\\\ \\\\omega=2\\\\pi f \\\\\\\\\\ v_{\\\\rm g}=\\\\frac{d\\\\omega}{dk}=v_{\\\\rm ph}+k\\\\frac{dv_{\\\\rm ph}}{dk}= v_{\\\\rm ph}\\\\left(1-\\\\frac{k}{n}\\\\frac{dn}{dk}\\\\right) \\\\\\\\\\ v=\\\\sqrt{\\\\kappa/\\\\varrho}</equation>. The meaning of symbol <equation>u</equation> in Wave Equation is: disturbance.", "tag": "physics,wave", "prompt": "Help me find the meaning of symbol <equation>u</equation> in Wave Equation?"}
{"completion": " The Latex Code for equation Youngs Modulusis <equation>\\\\Upsilon = \\\\frac{F/A}{\\\\Delta L/L} =\\\\frac{\\\\text{Stress}}{\\\\text{Strain}}</equation>", "tag": "physics,mechanics,youngs modulus", "prompt": "Can you write equation Youngs Modulus?"}
{"completion": " The equation for Optics Magnification is <equation>N=-\\\\frac{b}{v} \\\\\\\\\\ N_{\\\\alpha}=-\\\\frac{\\\\alpha_{\\\\rm syst}}{\\\\alpha_{\\\\rm none}}</equation>. The meaning of symbol <equation>\\displaystyle N=-\\frac{b}{v}</equation> in Optics Magnification is: linear magnification.", "tag": "physics,optics,magnification", "prompt": "What is the meaning of the symbol <equation>\\displaystyle N=-\\frac{b}{v}</equation> in Optics Magnification?"}
{"completion": " The Latex Code for equation State functions Maxwell Relationsis <equation>\\\\left(\\\\frac{\\\\partial T}{\\\\partial V}\\\\right)_{S}=-\\\\left(\\\\frac{\\\\partial p}{\\\\partial S}\\\\right)_{V}~,~~\\\\left(\\\\frac{\\\\partial T}{\\\\partial p}\\\\right)_{S}=\\\\left(\\\\frac{\\\\partial V}{\\\\partial S}\\\\right)_{p}~,~~ \\\\left(\\\\frac{\\\\partial p}{\\\\partial T}\\\\right)_{V}=\\\\left(\\\\frac{\\\\partial S}{\\\\partial V}\\\\right)_{T}~,~~\\\\left(\\\\frac{\\\\partial V}{\\\\partial T}\\\\right)_{p}=-\\\\left(\\\\frac{\\\\partial S}{\\\\partial p}\\\\right)_{T} \\\\\\\\\\ TdS=C_VdT+T\\\\left(\\\\frac{\\\\partial p}{\\\\partial T}\\\\right)_{V}dV~~\\\\mbox{and}~~TdS=C_pdT-T\\\\left(\\\\frac{\\\\partial V}{\\\\partial T}\\\\right)_{p}dp</equation>", "tag": "physics,thermodynamics", "prompt": "Can you write equation State functions Maxwell Relations?"}
{"completion": " The Latex Code for equation Operators in Quantum Physicsis <equation>\\\\int\\\\psi_1^*A\\\\psi_2d^3V=\\\\int\\\\psi_2(A\\\\psi_1)^*d^3V \\\\\\\\\\ A\\\\Psi=a\\\\Psi \\\\\\\\\\ \\\\Psi=\\\\sum\\\\limits_nc_nu_n \\\\\\\\\\ \\\\frac{dA}{dt}=\\\\frac{\\\\partial A}{\\\\partial t}+\\\\frac{[A,H]}{i\\\\hbar}</equation>", "tag": "physics,quantum", "prompt": "Can you write equation Operators in Quantum Physics?"}
{"completion": " The equation for Displacement of a slightly damped oscillator is: <equation>x = A_0 \\\\exp \\\\left( { - \\\\frac{b}{{2m}}t} \\\\right)\\\\cos \\\\left( {\\\\omega 't + \\\\delta } \\\\right)</equation>. Here is the brief introduction of Displacement of a slightly damped oscillator:\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,oscillations", "prompt": "Can you give me a brief introduction to Displacement of a slightly damped oscillator?"}
{"completion": " The equation for Angular Momentum is: <equation>M = I\\\\omega</equation>. Here is the brief introduction of Angular Momentum:\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,mechanics", "prompt": "Please give me detailed tutorial of Angular Momentum?"}
{"completion": " The Latex Code for equation Bending of light Snell's lawis <equation>n_i\\\\sin(\\\\theta_i)=n_t\\\\sin(\\\\theta_t) \\\\\\\\\\ \\\\frac{n_2}{n_1}=\\\\frac{\\\\lambda_1}{\\\\lambda_2}=\\\\frac{v_1}{v_2} \\\\\\\\\\ n^2=1+\\\\frac{n_{\\\\rm e}e^2}{\\\\varepsilon_0m}\\\\sum_j\\\\frac{f_j}{\\\\omega_{0,j}^2-\\\\omega^2-i\\\\delta\\\\omega} \\\\\\\\\\ v_{\\\\rm g}=c/(1+(n_{\\\\rm e}e^2/2\\\\varepsilon_0m\\\\omega^2))\\ </equation>", "tag": "physics,optics,Snell's law", "prompt": "How to write equation Bending of light Snell's law?"}
{"completion": " The related materials of Optics Magnification is: 1.Physics Formulary:<url>https://johanw.home.xs4all.nl/physics.pdf</url>;", "tag": "physics,optics,magnification", "prompt": "Can you help me find related materials of Optics Magnification?"}
{"completion": " The equation for Wave Equation is <equation>\\\\nabla^2u-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=\\\\frac{\\\\partial^2 u}{\\\\partial x^2}+\\\\frac{\\\\partial^2 u}{\\\\partial y^2}+\\\\frac{\\\\partial^2 u}{\\\\partial z^2}-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=0 \\\\\\\\\\ v=f\\\\lambda \\\\\\\\\\ k\\\\lambda=2\\\\pi \\\\\\\\\\ \\\\omega=2\\\\pi f \\\\\\\\\\ v_{\\\\rm g}=\\\\frac{d\\\\omega}{dk}=v_{\\\\rm ph}+k\\\\frac{dv_{\\\\rm ph}}{dk}= v_{\\\\rm ph}\\\\left(1-\\\\frac{k}{n}\\\\frac{dn}{dk}\\\\right) \\\\\\\\\\ v=\\\\sqrt{\\\\kappa/\\\\varrho}</equation>. The meaning of symbol <equation>n</equation> in Wave Equation is: refractive index of the medium.", "tag": "physics,wave", "prompt": "What does the symbol mean <equation>n</equation> in Wave Equation?"}
{"completion": " The equation for Mechanic Oscillations is <equation>m\\\\ddot{x}=F(t)-k\\\\dot{x}-Cx \\\\\\\\ \\ F(t)=\\\\hat{F}\\\\cos(\\\\omega t) \\\\\\\\ \\ -m\\\\omega^2 x=F-Cx-ik\\\\omega x \\\\\\\\ \\ \\\\omega_0^2=C/m \\\\\\\\ \\ x=\\\\frac{F}{m(\\\\omega_0^2-\\\\omega^2)+ik\\\\omega} \\\\\\\\ \\ \\\\dot{x}=\\\\frac{F}{i\\\\sqrt{Cm}\\\\delta+k} \\\\\\\\ \\ \\\\delta=\\\\frac{\\\\omega}{\\\\omega_0}-\\\\frac{\\\\omega_0}{\\\\omega} \\\\\\\\ \\ Z=F/\\\\dot{x} \\\\\\\\\\ Q=\\\\frac{\\\\sqrt{Cm}}{k}</equation>. The meaning of symbol <equation>F(t)</equation> in Mechanic Oscillations is: Periodic force.", "tag": "physics,mechanic,oscillations", "prompt": "What is the meaning of <equation>F(t)</equation> in Mechanic Oscillations?"}
{"completion": " The Latex Code for equation Thermodynamics Conservation of Energyis <equation>Q=\\\\Delta U+W \\\\\\\\\\ d\\\\hspace{-1ex}\\\\rule[1.25ex]{2mm}{0.4pt} Q=dU+d\\\\hspace{-1ex}\\\\rule[1.25ex]{2mm}{0.4pt}W \\\\\\\\\\ d\\\\hspace{-1ex}\\\\rule[1.25ex]{2mm}{0.4pt}W=pdV \\\\\\\\\\ Q=\\\\Delta H+W_{\\\\rm i}+\\\\Delta E_{\\\\rm kin}+\\\\Delta E_{\\\\rm pot}</equation>", "tag": "physics,thermodynamics", "prompt": "What is the latex code of equation Thermodynamics Conservation of Energy?"}
{"completion": " The equation for Waves In Long Conductors is <equation>Z_0=\\\\sqrt{\\\\frac{dL}{dx}\\\\frac{dx}{dC}} \\\\\\\\ v=\\\\sqrt{\\\\frac{dx}{dL}\\\\frac{dx}{dC}}</equation>. The meaning of symbol <equation>v=\\sqrt{\\frac{dx}{dL}\\frac{dx}{dC}}</equation> in Waves In Long Conductors is: is transmission velocity.", "tag": "physics,waves,oscillations", "prompt": "What does the symbol mean <equation>v=\\sqrt{\\frac{dx}{dL}\\frac{dx}{dC}}</equation> in Waves In Long Conductors?"}
{"completion": " The equation for Harmonic Oscillator Quantum is: <equation>H=\\\\frac{p^2}{2m}+\\\\frac{1}{2} m\\\\omega^2 x^2= \\\\frac{1}{2} \\\\hbar\\\\omega+\\\\omega A^\\\\dagger A \\\\\\\\\\ A=\\\\sqrt{\\\\mbox{$\\\\frac{1}{2}$}m\\\\omega}x+\\\\frac{ip}{\\\\sqrt{2m\\\\omega}} \\\\\\\\\\ A^\\\\dagger=\\\\sqrt{\\\\mbox{$\\\\frac{1}{2}$}m\\\\omega}x-\\\\frac{ip}{\\\\sqrt{2m\\\\omega}} \\\\\\\\\\ HAu_E=(E-\\\\hbar\\\\omega)Au_E \\\\\\\\\\ u_n=\\\\frac{1}{\\\\sqrt{n!}}\\\\left(\\\\frac{A^\\\\dagger}{\\\\sqrt{\\\\hbar}}\\\\right)^nu_0 \\\\\\\\\\ u_0=\\\\sqrt[4]{\\\\frac{m\\\\omega}{\\\\pi\\\\hbar}}\\\\exp\\\\left(-\\\\frac{m\\\\omega x^2}{2\\\\hbar}\\\\right) \\\\\\\\\\ E_n=( \\\\frac{1}{2} +n)\\\\hbar\\\\omega</equation>. Here is the brief introduction of Harmonic Oscillator Quantum:\n Latex code for the Parity Equation. If the wavefunction is split into even and odd functions, it can be expanded into eigenfunctions of P. I will briefly introduce the notations in this formulation. \n \n: Hamiltonian\n: Raising ladder operator\n: Lowering ladder operator\n: Eigenfunction for holds\n\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,quantum", "prompt": "I am interested in Harmonic Oscillator Quantum?"}
{"completion": " The Latex Code for equation Harmonic Oscillationsis <equation>\\\\Psi(t)=\\\\hat{\\\\Psi}(t)e^{i(\\\\omega t \\\\pm \\\\phi)}=\\\\hat{\\\\Psi}(t)\\\\cos (\\\\omega t \\\\pm \\\\phi) \\\\\\\\ \\ \\\\sum_{i} \\\\hat{\\\\Psi_{i}}\\\\cos(\\\\alpha_{i} \\\\pm \\\\omega t) =\\\\hat{\\\\Phi}\\\\cos (\\\\beta \\\\pm \\\\omega t) \\\\\\\\\\ \\\\tan (\\\\beta)=\\\\frac{\\\\sum_{i} \\\\hat{\\\\Psi_{i}} \\\\sin (\\\\alpha_{i})}{\\\\sum_{i} \\\\hat{\\\\Psi_{i}} \\\\cos (\\\\alpha_{i})} \\\\\\\\ \\ \\\\hat{\\\\Phi}^{2} = \\\\sum_{i} \\\\hat{\\\\Psi_{i}^{2}} + 2 \\\\sum_{j > i} \\\\sum_{i} \\\\hat{\\\\Psi_{i}} \\\\hat{\\\\Psi_{j}} \\\\cos (\\\\alpha_{i} - \\\\alpha_{j}) \\\\\\\\\\ \\\\int x(t) dt=\\\\frac{x(t)}{i \\\\omega} \\\\\\\\\\ \\\\frac{d^{n}(x(t))}{d t^{n}}=(i \\\\omega)^{n} x(t)</equation>", "tag": "physics,harmonic,oscillations", "prompt": "What is the equation of Harmonic Oscillations?"}
{"completion": " The Latex Code for equation Angular Momentumis <equation>M = I\\\\omega</equation>", "tag": "physics,mechanics", "prompt": "How to write equation Angular Momentum?"}
{"completion": " The equation for Bending of light Snell's law is <equation>n_i\\\\sin(\\\\theta_i)=n_t\\\\sin(\\\\theta_t) \\\\\\\\\\ \\\\frac{n_2}{n_1}=\\\\frac{\\\\lambda_1}{\\\\lambda_2}=\\\\frac{v_1}{v_2} \\\\\\\\\\ n^2=1+\\\\frac{n_{\\\\rm e}e^2}{\\\\varepsilon_0m}\\\\sum_j\\\\frac{f_j}{\\\\omega_{0,j}^2-\\\\omega^2-i\\\\delta\\\\omega} \\\\\\\\\\ v_{\\\\rm g}=c/(1+(n_{\\\\rm e}e^2/2\\\\varepsilon_0m\\\\omega^2))\\ </equation>. The meaning of symbol <equation>n</equation> in Bending of light Snell's law is: refractive index of the material.", "tag": "physics,optics,Snell's law", "prompt": "Can you explain the symbol <equation>n</equation> in Bending of light Snell's law?"}
{"completion": " The Latex Code for equation Displacement of a slightly damped oscillatoris <equation>x = A_0 \\\\exp \\\\left( { - \\\\frac{b}{{2m}}t} \\\\right)\\\\cos \\\\left( {\\\\omega 't + \\\\delta } \\\\right)</equation>", "tag": "physics,oscillations", "prompt": "What is the equation of Displacement of a slightly damped oscillator?"}
{"completion": " The equation for Operators in Quantum Physics is: <equation>\\\\int\\\\psi_1^*A\\\\psi_2d^3V=\\\\int\\\\psi_2(A\\\\psi_1)^*d^3V \\\\\\\\\\ A\\\\Psi=a\\\\Psi \\\\\\\\\\ \\\\Psi=\\\\sum\\\\limits_nc_nu_n \\\\\\\\\\ \\\\frac{dA}{dt}=\\\\frac{\\\\partial A}{\\\\partial t}+\\\\frac{[A,H]}{i\\\\hbar}</equation>. Here is the brief introduction of Operators in Quantum Physics:\n Latex code for Operators in Quantum Physics. I will briefly introduce the notations in this formulation. \n \n: Eigenvalue Equation\n: Eigenfunction\n: The time-dependence of an operator is given by (Heisenberg)\n\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,quantum", "prompt": "Can you explain Operators in Quantum Physics?"}
{"completion": " The equation for Optical System Matrix Methods is <equation>\\\\left(\\\\begin{array}{c}n_2\\\\alpha_2\\\\\\\\y_2\\\\end{array}\\\\right)=M \\\\left(\\\\begin{array}{c}n_1\\\\alpha_1\\\\\\\\y_1\\\\end{array}\\\\right) \\\\\\\\\\ {\\\\rm Tr}(M)=1</equation>. The meaning of symbol <equation>\\displaystyle M_{\\rm T}=\\left(\\begin{array}{cc}1&-D\\\\0&1\\end{array}\\right)</equation> in Optical System Matrix Methods is: TRefraction at a surface with dioptric power D.", "tag": "physics,optics,Matrix Methods", "prompt": "What is the meaning of the symbol <equation>\\displaystyle M_{\\rm T}=\\left(\\begin{array}{cc}1&-D\\\\0&1\\end{array}\\right)</equation> in Optical System Matrix Methods?"}
{"completion": " The equation for The Tunnel Effect is <equation>\\\\psi(x)=a^{-1/2}\\\\sin(kx) \\\\\\\\\\ E_n=n^2h^2/8a^2m \\\\\\\\\\ \\\\psi_1=A{\\\\rm e}^{ikx}+B{\\\\rm e}^{-ikx} \\\\\\\\ \\ \\\\psi_2=C{\\\\rm e}^{ik'x}+D{\\\\rm e}^{-ik'x} \\\\\\\\\\ \\\\psi_3=A'{\\\\rm e}^{ikx} \\\\\\\\\\ k'^2=2m(W-W_0)/\\\\hbar^2 \\\\\\ k^2=2mW \\\\\\\\\\ T=|A'|^2/|A|^2</equation>. The meaning of symbol <equation>\\psi(x)=a^{-1/2}\\sin(kx)</equation> in The Tunnel Effect is: Wavefunction of a particle in an infinitely high potential well.", "tag": "physics,quantum", "prompt": "Can you explain the symbol <equation>\\psi(x)=a^{-1/2}\\sin(kx)</equation> in The Tunnel Effect?"}
{"completion": " The equation for Simple Harmonic Motion Acceleration is: <equation>a = - \\\\omega ^2 x = - \\\\omega ^2 r\\\\sin (\\\\omega t)</equation>. Here is the brief introduction of Simple Harmonic Motion Acceleration:\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,mechanics", "prompt": "Please give me detailed tutorial of Simple Harmonic Motion Acceleration?"}
{"completion": " The equation for Optics Polarization is <equation>P=\\\\frac{I_{\\\\rm p}}{I_{\\\\rm p}+I_{\\\\rm u}}=\\\\frac{I_{\\\\rm max}-I_{\\\\rm min}}{I_{\\\\rm max}+I_{\\\\rm min}} \\\\\\\\\\ I(\\\\theta)=I(0)\\\\cos^2(\\\\theta)</equation>. The meaning of symbol <equation>\\theta</equation> in Optics Polarization is: is the angle of the polarizer.", "tag": "physics,optics,polarization", "prompt": "Can you explain the symbol <equation>\\theta</equation> in Optics Polarization?"}
{"completion": " The equation for Pendulums is <equation>T=1/f \\\\\\\\\\ T=2\\\\pi\\\\sqrt{m/C} \\\\\\\\\\ T=2\\\\pi\\\\sqrt{I/\\\\tau} \\\\\\\\\\ T=2\\\\pi\\\\sqrt{I/\\\\kappa} \\\\\\\\\\ T=2\\\\pi\\\\sqrt{l/g}</equation>. The meaning of symbol <equation>T=2\\pi\\sqrt{l/g}</equation> in Pendulums is: Mathematical pendulum.", "tag": "physics,pendulums", "prompt": "What does the symbol mean <equation>T=2\\pi\\sqrt{l/g}</equation> in Pendulums?"}
{"completion": " The equation for Quantum Wave Functions is <equation>\\\\Phi(k,t)=\\\\frac{1}{\\\\sqrt{h}}\\\\int\\\\Psi(x,t){\\\\rm e}^{-ikx}dx \\\\\\\\ \\ \\\\Psi(x,t)=\\\\frac{1}{\\\\sqrt{h}}\\\\int\\\\Phi(k,t){\\\\rm e}^{ikx}dk \\\\\\\\\\ v_{\\\\rm g}=p/m \\\\\\\\\\ E=\\\\hbar\\\\omega \\\\\\\\\\ \\\\left\\\\langle f(t) \\\\right\\\\rangle=\\\\int\\\\hspace{-1.5ex}\\\\int\\\\hspace{-1.5ex}\\\\int\\\\Psi^* f\\\\Psi d^3V \\\\\\\\ \\ \\\\left\\\\langle f_p(t) \\\\right\\\\rangle=\\\\int\\\\hspace{-1.5ex}\\\\int\\\\hspace{-1.5ex}\\\\int\\\\Phi^*f\\\\Phi d^3V_p \\\\\\\\\\ \\\\left\\\\langle f(t) \\\\right\\\\rangle=\\\\left\\\\langle \\\\Phi|f|\\\\Phi \\\\right\\\\rangle \\\\\\\\\\ \\\\left\\\\langle \\\\Phi|\\\\Phi \\\\right\\\\rangle=\\\\left\\\\langle \\\\Psi|\\\\Psi \\\\right\\\\rangle=1</equation>. The meaning of symbol <equation>\\left\\langle f \\right\\rangle</equation> in Quantum Wave Functions is: of a quantity f of a system..", "tag": "physics,quantum,wave", "prompt": "What is the meaning of <equation>\\left\\langle f \\right\\rangle</equation> in Quantum Wave Functions?"}
{"completion": " The equation for Phase constant of a driven oscillation is: <equation>\\\\tan \\\\delta = \\\\frac{{b\\\\omega }}{{m\\\\left( {\\\\omega _0^2 - \\\\omega ^2 } \\\\right)}}</equation>. Here is the brief introduction of Phase constant of a driven oscillation:\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,oscillation", "prompt": "I am interested in Phase constant of a driven oscillation?"}
{"completion": " The equation for Harmonic Oscillations is <equation>\\\\Psi(t)=\\\\hat{\\\\Psi}(t)e^{i(\\\\omega t \\\\pm \\\\phi)}=\\\\hat{\\\\Psi}(t)\\\\cos (\\\\omega t \\\\pm \\\\phi) \\\\\\\\ \\ \\\\sum_{i} \\\\hat{\\\\Psi_{i}}\\\\cos(\\\\alpha_{i} \\\\pm \\\\omega t) =\\\\hat{\\\\Phi}\\\\cos (\\\\beta \\\\pm \\\\omega t) \\\\\\\\\\ \\\\tan (\\\\beta)=\\\\frac{\\\\sum_{i} \\\\hat{\\\\Psi_{i}} \\\\sin (\\\\alpha_{i})}{\\\\sum_{i} \\\\hat{\\\\Psi_{i}} \\\\cos (\\\\alpha_{i})} \\\\\\\\ \\ \\\\hat{\\\\Phi}^{2} = \\\\sum_{i} \\\\hat{\\\\Psi_{i}^{2}} + 2 \\\\sum_{j > i} \\\\sum_{i} \\\\hat{\\\\Psi_{i}} \\\\hat{\\\\Psi_{j}} \\\\cos (\\\\alpha_{i} - \\\\alpha_{j}) \\\\\\\\\\ \\\\int x(t) dt=\\\\frac{x(t)}{i \\\\omega} \\\\\\\\\\ \\\\frac{d^{n}(x(t))}{d t^{n}}=(i \\\\omega)^{n} x(t)</equation>. The meaning of symbol <equation>\\hat{\\Psi_{i}}</equation> in Harmonic Oscillations is: Amplitude.", "tag": "physics,harmonic,oscillations", "prompt": "Can you explain the symbol <equation>\\hat{\\Psi_{i}}</equation> in Harmonic Oscillations?"}
{"completion": " The Latex Code for equation Shear Modulusis <equation>M_{s} = \\\\frac{F_{s} / A}{ {\\\\Delta x} /L}=\\\\frac{F_{s}/A}{\\\\tan \\\\theta}M_{s} = \\\\frac{F_{s}/A}{\\\\Delta x/L} = \\\\frac{F_{s}/A}{\\\\tan \\\\theta}</equation>", "tag": "physics,mechanics,shear modulus", "prompt": "Please give me some hints on equation Shear Modulus?"}
{"completion": " The equation for Diffraction is <equation>\\\\frac{I(\\\\theta)}{I_0}=\\\\left(\\\\frac{\\\\sin(u)}{u}\\\\right)^2\\\\cdot \\\\left(\\\\frac{\\\\sin(Nv)}{\\\\sin(v)}\\\\right)^2 \\\\\\\\\\ u=\\\\pi b\\\\sin(\\\\theta)/\\\\lambda \\\\\\\\\\ v=\\\\pi d\\\\sin(\\\\theta)/\\\\lambda</equation>. The meaning of symbol <equation>d\\sin(\\theta)=k\\lambda</equation> in Diffraction is: is the maxima in intensity.", "tag": "physics,optics,diffraction", "prompt": "Help me find the meaning of symbol <equation>d\\sin(\\theta)=k\\lambda</equation> in Diffraction?"}
{"completion": " The equation for Prisms and Dispersion is <equation>\\\\delta=\\\\theta_i+\\\\theta_{i'}+\\\\alpha \\\\\\\\\\ n=\\\\frac{\\\\sin(\\\\frac{1}{2}(\\\\delta_{\\\\rm min}+\\\\alpha))}{\\\\sin(\\\\frac{1}{2}\\\\alpha)} \\\\\\\\\\ D=\\\\frac{d\\\\delta}{d\\\\lambda}=\\\\frac{d\\\\delta}{dn}\\\\frac{dn}{d\\\\lambda} \\\\\\\\\\ \\\\frac{d\\\\delta}{dn}=\\\\frac{2\\\\sin(\\\\frac{1}{2}\\\\alpha)}{\\\\cos(\\\\frac{1}{2}(\\\\delta_{\\\\rm min}+\\\\alpha))}</equation>. The meaning of symbol <equation>\\alpha</equation> in Prisms and Dispersion is: is apex angle.", "tag": "physics,optics,prisms,dispersion", "prompt": "Help me find the meaning of symbol <equation>\\alpha</equation> in Prisms and Dispersion?"}
{"completion": " The equation for General Relativity is: <equation>\\\\frac{\\\\mathrm{d}^{2} x^{\\\\alpha}}{\\\\mathrm{d} s^{2}}+\\\\Gamma^{\\\\alpha}_{\\\\beta\\\\gamma}\\\\frac{\\\\mathrm{d} x^{\\\\beta}}{\\\\mathrm{d} s}\\\\frac{\\\\mathrm{d} x^{\\\\gamma}}{\\\\mathrm{d} s}=0</equation>. Here is the brief introduction of General Relativity:Latex code for the principles of general relativity. I will briefly introduce the notations in this formulation. ", "tag": "physics,relativity", "prompt": "I am interested in General Relativity?"}
{"completion": " The Latex Code for equation Optical System Matrix Methodsis <equation>\\\\left(\\\\begin{array}{c}n_2\\\\alpha_2\\\\\\\\y_2\\\\end{array}\\\\right)=M \\\\left(\\\\begin{array}{c}n_1\\\\alpha_1\\\\\\\\y_1\\\\end{array}\\\\right) \\\\\\\\\\ {\\\\rm Tr}(M)=1</equation>", "tag": "physics,optics,Matrix Methods", "prompt": "What is the equation of Optical System Matrix Methods?"}
{"completion": " The Latex Code for equation The general solution of Wave Equationis <equation>\\\\frac{\\\\partial^2 u(x,t)}{\\\\partial t^2}=\\\\sum_{m=0}^{N}\\\\left(b_m\\\\frac{\\\\partial ^m}{\\\\partial x^m}\\\\right)u(x,t) \\\\\\\\ \\ u(x,t)=\\\\int\\\\limits_{-\\\\infty}^{\\\\infty}\\\\left(a(k){\\\\rm e}^{i(kx-\\\\omega_1(k)t)}+ b(k){\\\\rm e}^{i(kx-\\\\omega_2(k)t)}\\\\right)dk \\\\\\\\\\ u(x,t)=A{\\\\rm e}^{i(kx-\\\\omega t)} \\\\\\\\\\ \\\\omega_j=\\\\omega_j(k)</equation>", "tag": "physics,general solution,waves", "prompt": "What is the latex code of equation The general solution of Wave Equation?"}
{"completion": " The Latex Code for equation The Stationary Phase Method Wave Equationis <equation>\\\\int\\\\limits_{-\\\\infty}^\\\\infty a(k){\\\\rm e}^{i(kx-\\\\omega(k)t)}dk\\\\approx \\\\sum_{i=1}^{N}\\\\sqrt{\\\\frac{2\\\\pi}{\\\\frac{d^2\\\\omega(k_i)}{dk_i^2}}} \\\\exp\\\\left[-i\\\\mbox{$\\\\frac{1}{4}$}\\\\pi+i(k_ix-\\\\omega(k_i)t)\\\\right]</equation>", "tag": "physics,stationary phase", "prompt": "Show me the latex code of equation The Stationary Phase Method Wave Equation?"}
{"completion": " The equation for Waves In Long Conductors is: <equation>Z_0=\\\\sqrt{\\\\frac{dL}{dx}\\\\frac{dx}{dC}} \\\\\\\\ v=\\\\sqrt{\\\\frac{dx}{dL}\\\\frac{dx}{dC}}</equation>. Here is the brief introduction of Waves In Long Conductors:\n Latex code for the Waves in Long conductors. I will briefly introduce the notations in this formulation. \n \n: is transmission velocity\n\n\nRelated Documents\n\nPhysics Formulary\nOscillations of Mechanical Systems\n\nRelated Videos\n\n\n", "tag": "physics,waves,oscillations", "prompt": "Please give me detailed tutorial of Waves In Long Conductors?"}
{"completion": " The equation for The general solution of Wave Equation is: <equation>\\\\frac{\\\\partial^2 u(x,t)}{\\\\partial t^2}=\\\\sum_{m=0}^{N}\\\\left(b_m\\\\frac{\\\\partial ^m}{\\\\partial x^m}\\\\right)u(x,t) \\\\\\\\ \\ u(x,t)=\\\\int\\\\limits_{-\\\\infty}^{\\\\infty}\\\\left(a(k){\\\\rm e}^{i(kx-\\\\omega_1(k)t)}+ b(k){\\\\rm e}^{i(kx-\\\\omega_2(k)t)}\\\\right)dk \\\\\\\\\\ u(x,t)=A{\\\\rm e}^{i(kx-\\\\omega t)} \\\\\\\\\\ \\\\omega_j=\\\\omega_j(k)</equation>. Here is the brief introduction of The general solution of Wave Equation:\n The general solution of is given by above.\n \n\n\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,general solution,waves", "prompt": "What's the meaning of The general solution of Wave Equation?"}
{"completion": " The equation for Wave Equation is <equation>\\\\nabla^2u-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=\\\\frac{\\\\partial^2 u}{\\\\partial x^2}+\\\\frac{\\\\partial^2 u}{\\\\partial y^2}+\\\\frac{\\\\partial^2 u}{\\\\partial z^2}-\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}=0 \\\\\\\\\\ v=f\\\\lambda \\\\\\\\\\ k\\\\lambda=2\\\\pi \\\\\\\\\\ \\\\omega=2\\\\pi f \\\\\\\\\\ v_{\\\\rm g}=\\\\frac{d\\\\omega}{dk}=v_{\\\\rm ph}+k\\\\frac{dv_{\\\\rm ph}}{dk}= v_{\\\\rm ph}\\\\left(1-\\\\frac{k}{n}\\\\frac{dn}{dk}\\\\right) \\\\\\\\\\ v=\\\\sqrt{\\\\kappa/\\\\varrho}</equation>. The meaning of symbol <equation>v=\\sqrt{\\gamma p/\\varrho}=\\sqrt{\\gamma RT/M}</equation> in Wave Equation is: Further for pressure waves in a gas.", "tag": "physics,wave", "prompt": "Can you explain the symbol <equation>v=\\sqrt{\\gamma p/\\varrho}=\\sqrt{\\gamma RT/M}</equation> in Wave Equation?"}
{"completion": " The equation for Thermodynamics Ideal Mixtures is <equation>U_{\\\\rm mixture}=\\\\sum_i n_i U^0_i \\\\\\\\ \\ H_{\\\\rm mixture}=\\\\sum_i n_i H^0_i \\\\\\\\ \\ S_{\\\\rm mixture}=n\\\\sum_i x_i S^0_i+\\\\Delta S_{\\\\rm mix} \\\\\\\\\\ \\\\Delta S_{\\\\rm mix}=-nR\\\\sum\\\\limits_i x_i\\\\ln(x_i)</equation>. The meaning of symbol <equation>\\Delta T_{\\rm k}=\\frac{RT_{\\rm k}^2}{r_{\\beta\\alpha}}x_2~~,~~ \\Delta T_{\\rm s}=-\\frac{RT_{\\rm s}^2}{r_{\\gamma\\beta}}x_2</equation> in Thermodynamics Ideal Mixtures is: one component in a second gives rise to decrease of the freezing point.", "tag": "physics,thermodynamics,ideal mixtures", "prompt": "Can you explain the symbol <equation>\\Delta T_{\\rm k}=\\frac{RT_{\\rm k}^2}{r_{\\beta\\alpha}}x_2~~,~~ \\Delta T_{\\rm s}=-\\frac{RT_{\\rm s}^2}{r_{\\gamma\\beta}}x_2</equation> in Thermodynamics Ideal Mixtures?"}
{"completion": " The equation for Waveguides and resonating cavities is: <equation>\\\\begin{array}{ll} \\\\vec{n}\\\\cdot(\\\\vec{D}_2-\\\\vec{D}_1)=\\\\sigma~~&~~\\\\vec{n}\\\\times(\\\\vec{E}_2-\\\\vec{E}_1)=0\\\\\\\\ \\\\vec{n}\\\\cdot(\\\\vec{B}_2-\\\\vec{B}_1)=0~~&~~\\\\vec{n}\\\\times(\\\\vec{H}_2-\\\\vec{H}_1)=\\\\vec{K} \\\\end{array} \\\\\\\\ \\\\vec{E}(\\\\vec{x},t)=\\\\vec{\\\\cal E}(x,y){e}^{i(kz-\\\\omega t)} \\\\\\\\ \\\\vec{B}(\\\\vec{x},t)=\\\\vec{\\\\cal{B}}(x,y){e}^{i(kz-\\\\omega t)}</equation>. Here is the brief introduction of Waveguides and resonating cavities:\n\n\n\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,waveguides", "prompt": "I am interested in Waveguides and resonating cavities?"}
{"completion": " The equation for Cylindrical Waves is: <equation>\\\\frac{1}{v^2}\\\\frac{\\\\partial^2 u}{\\\\partial t^2}-\\\\frac{1}{r}\\\\frac{\\\\partial }{\\\\partial r}\\\\left(r\\\\frac{\\\\partial u}{\\\\partial r}\\\\right)=0 \\\\\\\\\\ u(r,t)=\\\\frac{\\\\hat{u}}{\\\\sqrt{r}}\\\\cos(k(r\\\\pm vt))</equation>. Here is the brief introduction of Cylindrical Waves:\n When the wave is cylindrical symmetry, the homogeneous wave equation becomes as above. This is a Bessel equation, with solutions that can be written as Hankel functions. For sufficient large values of r.\n \n\n\n\nRelated Documents\n\nPhysics Formulary\n\nRelated Videos\n\n\n", "tag": "physics,cylindrical waves", "prompt": "Can you give me a brief introduction to Cylindrical Waves?"}