# Reflection coefficient of the step function potential

1. Mar 8, 2010

### kakarotyjn

1. The problem statement, all variables and given/known data
Consider the step function potential: $$V(x) = \{ \begin{array}{*{20}c} {0,(x \le 0)} \\ {V_0 ,(x > 0)} \\ \end{array}$$,Caculate the reflection coefficient,for the case E<V0,and comment on the answer

2. Relevant equations
$$- \frac{{\hbar ^2 }}{{2m}}\frac{{d^2 \psi }}{{dx^2 }} + V_0 \psi = E\psi$$

3. The attempt at a solution
when x<=0,let $$k = \frac{{\sqrt {2mE} }}{\hbar }$$,then $$\psi (x) = Ae^{kxi} + Be^{ - kxi}$$,if x>0,then let $$l = \frac{{\sqrt {2m(V_0 - E)} }}{\hbar }$$,and $$\psi (x) = De^{ - lx}$$

Then how do we explain it?The funtion is real in the right

Last edited: Mar 8, 2010
2. Mar 8, 2010

### vela

Staff Emeritus
So far, all you've done is written down the solutions to the wave equation in two regions. What's the next step? What's the definition of the reflection coefficient?

3. Mar 9, 2010

### kakarotyjn

In the book,if psi(x) is not real in the right and left,then we can find the transmission and reflection coefficient.But in this question,it's not all complex.

definition of the reflection coefficient?You must know Quantum Tunneliing.it that one

4. Mar 9, 2010

### vela

Staff Emeritus
I know what the reflection coefficient is. It's not clear to me that you did from your initial post.

It doesn't matter if all the solutions are not complex. The next step is the same: match the wavefunction and its derivative at the boundary.

5. Mar 9, 2010

### kakarotyjn

Thanks very much.But why?how should we think about it?