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Potential step, classical vs quantum mechanics

  1. Apr 30, 2012 #1
    1. The problem statement, all variables and given/known data

    We have the potential step

    [itex]U(x) = 0, \ x < 0
    \\ U(x) = U_0, \ x>0 [/itex]

    2. Relevant equations & 3. The attempt at a solution

    If we measure, for example, the magnitude of the transmitted current [itex]j_T[/itex] over the reflected current [itex]j_R[/itex], so

    [itex]\left| \dfrac{j_T}{j_R} \right| [/itex]

    then classically we would expect no reflection for [itex]x<0[/itex], so we would have the reflected current as 0, whereas here if that were the case then... would this ratio be infinite?

    I'm not sure if this is correct. I believe that the ratio involving the current of the incident and reflected [itex]\left| \dfrac{j_R}{j_{inc}} \right| [/itex] should classically be 0 since there's no reflected wave.

    Just wanted to double check, really!
     
  2. jcsd
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