Why Does Reflection Occur at a Lower Potential in Quantum Mechanics?

[tarq]

Homework Statement

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.

Homework Equations

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, what's confusing me is that as E tends to V, R tends to 1 which doesn't 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!

 

[Jhero]

Thank you for your question. It seems like you have made a mistake in your calculation. The reflection coefficient for particles incident on a one dimensional step function potential with energy E>V should be R=1, as the particles will all be reflected at the step down in potential. This makes sense intuitively, as the potential barrier is higher than the energy of the particles, so they cannot pass through it. I suggest checking your calculations and making sure you have implemented the boundary conditions correctly. Let me know if you need any further assistance. Good luck with your studies!