# Step potential

## Homework Statement

I'm working through a step potential and I am confused as to why one of the coefficients doesn't go to zero.

V(x) = 0 when x < 0;
V(x) = V_not when x > 0;

a. Calculate reflection coefficient when E < V_not
I can solve the reflection part, it is a step towards it that i am confused about.

## The Attempt at a Solution

Now i know the solutions solve to:

Aexp(ikx)+Bexp(-ikx) where k= sqrt(2mE)/hbar when x<0
Cexp(lx) where l=sqrt(-2m(E-V_not)/hbar when x>0

So my question is why doesn't B=0? Because when x->-infinity it goes to infinity so B has to be 0. The only reason i can think it wouldn't is because of tunneling. If this is the case how do I spot this. Is it only relevant in step potentials?

vela
Staff Emeritus
Homework Helper
e-ikx is oscillatory. It doesn't blow up as x goes to -∞.

Ah thank you. Now that brings up another question for the same problem but now E>Vo.

The wave equations go to:
Aexp(ikx) + Bexp(-ikx) when x < 0. k=sqrt(2mE)/hbar
Cexp(ilx) + Dexp(-ilx) when x > 0. l=sqrt(2m(E-Vo))/hbar

Now in this case why does D=0.

vela
Staff Emeritus