# QM step potential problem

1. Apr 16, 2009

### tarq

1. The problem statement, all variables and given/known data

Consider particles incident on a one dimensional step function potential, V(x)=Vphi(x) with energy E>V. Calculate the reflection coefficent for particles incident from the right (Barrier height=V at x>0, Barrier height=0 at x<0). Consider the limits as E tends to V and E tends to infinity.

2. Relevant equations

3. The attempt at a solution

Okay the question seemed pretty simple and i worked out the solutions to the wave equation and then used these to find the reflectio coefficent and implemented the boundary conditions to give the solution to me in terms of k. the solution i got was R=(K-1)^2/(K+1)^2 where K=sqrt(1-V/E). This means as E tends to infinity K tends to 1 and R tends to zero which makes sense, whats confusing me is that as E tends to V, R tends to 1 which doesnt seem to make any sense as the particles are approaching a step down in the potential. I would think that the particles are moving along the potential and then would 'fall down' at the step rather than be reflected because they arent hitting a wall and so i think my answer must be wrong!