Potential Step (wave amplitude)

[solas99]

1. If the incident wave is coming from LHS,
what happens to the wave amplitude on the RHS when electron energy is equal V₀?

2. the wavevectors on both sides of the step are different (generally), is there an energy at which the have the same magnitude?

thanks for any help..

 

[mfb]

1. If the incident wave is coming from LHS,
what happens to the wave amplitude on the RHS when electron energy is equal V₀?

The usual way to analyse this problem uses assumptions about the electrons which cannot be satisfied in reality (especially: electrons with a single, fixed energy). And here you have a case where you can see this flaw.
If you have a free electron which "moves", it cannot have a single energy value, it has some distribution. The parts above V₀ can (partially) go through, the other parts are reflected. If your electron does not "move", the question is ill-defined.

2. the wavevectors on both sides of the step are different (generally), is there an energy at which the have the same magnitude?

With low energy, everything gets reflected, with high energy, nearly everything is transmitted. So somewhere in between, you have 1/2 on both sides.