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

Equation



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.

  • : Wavefunction of a particle in an infinitely high potential well
  • : The energy levels
  • : If 1, 2 and 3 are the areas in front, within and behind the potential well

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