(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the reflection coefficient for electrons traveling toward a potential change from [tex]V[/tex] to [tex]V_0[/tex] with a total energy [tex]E > V_0[/tex].

The potential diagram is just a unit step function. It goes from [tex]V = 0[/tex] to [tex]V = V_0[/tex] at [tex]x=0[/tex]. In piecewise notation:

[tex]

\begin{displaymath}

V(x) = \left\{

\begin{array}{lr}

0 & : x < 0 \\

V_0 & : x \ge 0

\end{array}

\right.

\end{displaymath}

[/tex]

The piecewise notation does not account for the [tex]V(x)[/tex] being continuous at [tex]x=0[/tex].

2. Relevant equations

a) Probability flux:

[tex]S\left( x,t \right)=-\frac{i\hbar}{2m}\left[ \Psi^*\left( x,t \right) \frac{\partial \Psi\left( x,t \right)}{\partial x} - \Psi\left( x,t \right) \frac{\partial \Psi^*\left( x,t \right)}{\partial x}\left][/tex]

b) Reflection coefficient:

[tex]R=\frac{S_{I}^{-x}\left( x,t \right)}{S_{I}^{+x}\left( x,t \right)}[/tex]

3. The attempt at a solution

I've solved for the wave equations at [tex]x > 0[/tex] and [tex]x < 0[/tex]. I'm stuck as far as where to go from there.

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# Homework Help: Reflection Coeff - Quantum Mech

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