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Quantum Mechanics - Question about the Finite Square Well

  1. May 1, 2017 #1
    Hi,

    I'm preparing for an exam, and I'm going over past papers. I've solved parts a & b of this question without any problems, however I'm finding it hard to understand part c.

    phyqm.png

    I thought of shifting the boundary conditions so I'd have 0 and L in the place of ± L/2, but that would not work because the boundary condition to solve the consistency condition requires x = L/2.
    Could I get some pointers on where to start? I'm incredibly lost.
     
  2. jcsd
  3. May 1, 2017 #2

    Dr Transport

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    if [itex] V = 0[/itex] for [itex] x < 0 [/itex] think about where the nodes of the wave function are for an infinite well....
     
  4. May 1, 2017 #3
    Between [itex] x = 0[/itex] and [itex] x = L/2 [/itex]?
     
  5. May 1, 2017 #4

    Dr Transport

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    draw the wave functions for an infinite well, where does the central node cross the energy line??
     
  6. May 2, 2017 #5
    Alright, I think I have finally figured out the question.

    So, before, I had V = 0 for x < -L/2, V = 0 for x > L/2, and V = -Vo for -L/2 < x < L/2.

    If the potential is modified such that x < 0 is V = ∞. I'd still have V = -Vo for 0 < x < L/2. and V = 0 for x > L/2
    This means that the wavefunction for region 3 (x > L/2) would still hold the same as in part b, and for 0 < x < L/2 the wavefunction would be the same as in the classically allowed region as in part b. So when I apply the boundary condition at x = L/2 I'm going to get the same consistency condition seen in part b, as required.
     
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