# Homework Help: Reflection Coeff - Quantum Mech

1. Apr 8, 2010

### nickmai123

1. The problem statement, all variables and given/known data
Find the reflection coefficient for electrons traveling toward a potential change from $$V$$ to $$V_0$$ with a total energy $$E > V_0$$.
The potential diagram is just a unit step function. It goes from $$V = 0$$ to $$V = V_0$$ at $$x=0$$. In piecewise notation:
$$\begin{displaymath} V(x) = \left\{ \begin{array}{lr} 0 & : x < 0 \\ V_0 & : x \ge 0 \end{array} \right. \end{displaymath}$$
The piecewise notation does not account for the $$V(x)$$ being continuous at $$x=0$$.

2. Relevant equations
a) Probability flux:
$$S\left( x,t \right)=-\frac{i\hbar}{2m}\left[ \Psi^*\left( x,t \right) \frac{\partial \Psi\left( x,t \right)}{\partial x} - \Psi\left( x,t \right) \frac{\partial \Psi^*\left( x,t \right)}{\partial x}\left]$$

b) Reflection coefficient:
$$R=\frac{S_{I}^{-x}\left( x,t \right)}{S_{I}^{+x}\left( x,t \right)}$$

3. The attempt at a solution
I've solved for the wave equations at $$x > 0$$ and $$x < 0$$. I'm stuck as far as where to go from there.

2. Apr 8, 2010

### nickjer

Are you asking for help on (a)? Can you also show us your final wave function? And have you tried plugging that wavefunction into (a)?

3. Apr 8, 2010

### vela

Staff Emeritus
Require continuity of the wavefunction and its derivative at x=0. That will allow you to solve for most of the constants.