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Homework Help: Potential Barrier (Q.M. vs Classical Phy.)

  1. Mar 16, 2007 #1
    If you have a Potential Barrier V (width a) and particles incident on left with energy E where E>V, are the following true:

    Classical Physics:
    - All particles will be transmitted past the barrier
    - It cannot be reflected because that would mean it has negative E which is not possible.

    Quantum Mecahnically:
    - Some particles will be reflected (due to there wave nature)
    - Some particles will be transmitted
    - Some particles may exist in the barrier
    - Resonant modes exist for 100% transmission of particles

    Am I missing anything important?
     
  2. jcsd
  3. Mar 21, 2007 #2
    In order:

    Classical Physics:
    - Yes
    - You are correct that it cannot be reflected in the case of E>V but this has nothing to do with negative energy, rather it is reflected if E<V. Moreover, you can have a negative energy if your potential is defined for negative values. (In fact, potentials are often defined such that bound states correspond to negative energies.)

    Quantum mechanically:
    - Yes
    - Yes
    - Yes, but only if E<V (the opposite of your stated case) and if your barrier is a well and not a step.
    - Not so sure about the resonant modes part.

    Now someone else can check to see if I missed anything important.
     
    Last edited: Mar 21, 2007
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