Quantum Wave Functions Equation Formula Latex Code and Summary

Quantum Wave Functions

Tags: #physics #quantum #wave

Equation

$$\Phi(k,t)=\frac{1}{\sqrt{h}}\int\Psi(x,t){\rm e}^{-ikx}dx \\ \Psi(x,t)=\frac{1}{\sqrt{h}}\int\Phi(k,t){\rm e}^{ikx}dk \\ v_{\rm g}=p/m \\ E=\hbar\omega \\ \left\langle f(t) \right\rangle=\int\hspace{-1.5ex}\int\hspace{-1.5ex}\int\Psi^* f\Psi d^3V \\ \left\langle f_p(t) \right\rangle=\int\hspace{-1.5ex}\int\hspace{-1.5ex}\int\Phi^*f\Phi d^3V_p \\ \left\langle f(t) \right\rangle=\left\langle \Phi|f|\Phi \right\rangle \\ \left\langle \Phi|\Phi \right\rangle=\left\langle \Psi|\Psi \right\rangle=1$$

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

$\Phi(k,t)=\frac{1}{\sqrt{h}}\int\Psi(x,t){\rm e}^{-ikx}dx \\ \Psi(x,t)=\frac{1}{\sqrt{h}}\int\Phi(k,t){\rm e}^{ikx}dk \\ v_{\rm g}=p/m \\ E=\hbar\omega \\ \left\langle f(t) \right\rangle=\int\hspace{-1.5ex}\int\hspace{-1.5ex}\int\Psi^* f\Psi d^3V \\ \left\langle f_p(t) \right\rangle=\int\hspace{-1.5ex}\int\hspace{-1.5ex}\int\Phi^*f\Phi d^3V_p \\ \left\langle f(t) \right\rangle=\left\langle \Phi|f|\Phi \right\rangle \\ \left\langle \Phi|\Phi \right\rangle=\left\langle \Psi|\Psi \right\rangle=1$

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

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.

$\psi$ : Wave Function
$v_{\rm g}=p/m$ : Group Velocity
$E=\hbar\omega$ : Energy
$\left\langle f \right\rangle$ : Measure with the probability P of finding a particle somewhere. The expectation value
$\left\langle f \right\rangle$ of a quantity f of a system.

Discussion

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Damon Dalton

I have my heart set on passing this test.

2023-02-23 00:00
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Susan Miller reply to Damon Dalton

Gooood Luck, Man!

2023-03-11 00:00:00.0
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Theresa Rivera

I hope my efforts are enough to pass this exam.

2023-01-11 00:00
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Christopher Martinez reply to Theresa Rivera

Nice~

2023-01-15 00:00:00.0
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Deborah Lewis

My focus is on getting a pass for this test.

2023-03-13 00:00
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Neil Richmond reply to Deborah Lewis

Gooood Luck, Man!

2023-04-01 00:00:00.0
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