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Homework Help: Step down potential

  1. Jun 21, 2007 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations
    Various exponential equations and equations for wavenumber K

    3. The attempt at a solution
    Ok the thing im 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 im not sure. If theres 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 doesnt 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?

  2. jcsd
  3. Jun 21, 2007 #2


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    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.
  4. Jun 22, 2007 #3
    Yeh great way to help my confidence, make me feel stupid. Thanks for the info.
  5. Jun 22, 2007 #4


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    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'.
  6. Jun 22, 2007 #5
    no worries
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