Step Down Potential Homework: Electron Beam Incident on V(x)

[FunkyDwarf]

Homework Statement

A beam of electrons with number density 10^15 electrons/m is incident from the left on the step potential energy

V(x) = 0 for x< 0 and
-V(nought) for x > 0
The constant is positive so its a step down

Homework Equations

Various exponential equations and equations for wavenumber K

The Attempt at a Solution

Ok the thing I am confused about here is as follows: can we assume that E > V? i mean i would have said yes because you can't have something with negative energy, but then again the potential is effectively negative so I am not sure. If there's the case of E>v and E<V do we split it up into two cases? namley one where a decay occurs in the area where V = 0 (i know normally this doesn't happen but i assume we consider it relative to its surrounding, ie a lower potential) and another case where all that happens is the wavenumber changes and you still have two sets of standing waves.

Also we are asked to find the reflection and transmission coefficients: will these simply be the amplitudes of the exponentials going in certain directions?

Thanks!
-G

 

[Dick]

The incoming wave is coming from the V=0 side, so you can assume E>0. Put in your boundary conditions (no incoming wave from the right etc), normalize flux, match amplitude and derivatives at the boundary. Transmission coefficient is then the ratio squared of the amplitude of the incoming wave to the outgoing wave. This is pretty standard stuff.

 

[FunkyDwarf]

This is pretty standard stuff.

Yeh great way to help my confidence, make me feel stupid. Thanks for the info.

 

[Dick]

Yeh great way to help my confidence, make me feel stupid. Thanks for the info.

Sorry, guess what I meant to say is that it is easy to find references and detailed solutions to problems like this. I had to look one up to remind myself how the parts worked as well. Didn't mean to imply it was 'obvious'. Just 'standard'.

 

[FunkyDwarf]

no worries