Quantum Wave Functions
Tags: #physics #quantum #waveEquation
$$\Phi(k,t)=\frac{1}{\sqrt{h}}\int\Psi(x,t){\rm e}^{-ikx}dx \\ \Psi(x,t)=\frac{1}{\sqrt{h}}\int\Phi(k,t){\rm e}^{ikx}dk \\ v_{\rm g}=p/m \\ E=\hbar\omega \\ \left\langle f(t) \right\rangle=\int\hspace{-1.5ex}\int\hspace{-1.5ex}\int\Psi^* f\Psi d^3V \\ \left\langle f_p(t) \right\rangle=\int\hspace{-1.5ex}\int\hspace{-1.5ex}\int\Phi^*f\Phi d^3V_p \\ \left\langle f(t) \right\rangle=\left\langle \Phi|f|\Phi \right\rangle \\ \left\langle \Phi|\Phi \right\rangle=\left\langle \Psi|\Psi \right\rangle=1$$Latex Code
\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
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Introduction
Equation
Latex Code
\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
Explanation
Latex code for Quantum Wave Functions. If light is considered to consist of particles, the wavelength of scattered light can be derived as above. I will briefly introduce the notations in this formulation.
: Wave Function
: Group Velocity
: Energy
: Measure with the probability P of finding a particle somewhere. The expectation value
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