The Tunnel Effect Equation Formula Latex Code and Summary

The Tunnel Effect

Tags: #physics #quantum

Equation

$$\psi(x)=a^{-1/2}\sin(kx) \\ E_n=n^2h^2/8a^2m \\ \psi_1=A{\rm e}^{ikx}+B{\rm e}^{-ikx} \\ \psi_2=C{\rm e}^{ik'x}+D{\rm e}^{-ik'x} \\ \psi_3=A'{\rm e}^{ikx} \\ k'^2=2m(W-W_0)/\hbar^2 \ k^2=2mW \\ T=|A'|^2/|A|^2$$

Latex Code

                                 \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

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Introduction

$\psi(x)=a^{-1/2}\sin(kx) \\ E_n=n^2h^2/8a^2m \\ \psi_1=A{\rm e}^{ikx}+B{\rm e}^{-ikx} \\ \psi_2=C{\rm e}^{ik'x}+D{\rm e}^{-ik'x} \\ \psi_3=A'{\rm e}^{ikx} \\ k'^2=2m(W-W_0)/\hbar^2 \ \\ k^2=2mW \\ T=|A'|^2/|A|^2$

Latex Code

            \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

Explanation

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.

$\psi(x)=a^{-1/2}\sin(kx)$ : Wavefunction of a particle in an infinitely high potential well
$E_n=n^2h^2/8a^2m$ : The energy levels
$\psi_1,\psi_2,\psi_3$ : If 1, 2 and 3 are the areas in front, within and behind the potential well

Discussion

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Betty Taylor

May luck be on my side to pass this exam.

2023-07-27 00:00
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Best Wishes.

2023-08-23 00:00:00.0
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George Lewis

I've done everything I can, now I just need to pass this exam.

2024-04-20 00:00
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Les Finch reply to George Lewis

Best Wishes.

2024-05-11 00:00:00.0
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Betty Taylor

Working hard in hopes of passing this test.

2023-12-19 00:00
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You can make it...

2024-01-11 00:00:00.0
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