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Quantum Mechanics: Outside a (in)Finite Well

  1. Aug 12, 2017 #1
    1. The problem statement, all variables and given/known data
    Referencing image attached.

    Screen Shot 2017-08-12 at 3.35.11 PM.png

    I'm not sure how the example arrived at ψ ⇒ 0 at x<0 and >L as K ⇒ ∞ in the limiting case of an infinite potential well.

    2. Relevant equations


    3. The attempt at a solution

    I tried simply applying limits to the wavefuction but in the case x<0, the answer I was arriving at was simply ∞ as the term with constant C approaches 0 and the term with constant D approaches ∞.

    I'm also clueless as how ψ ⇒ 0 for x>L.

    Can anyone help point out what I'm missing? Thanks in advance.
     
  2. jcsd
  3. Aug 12, 2017 #2

    BvU

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    Hi,
    From the explanation at (b) you see that D = 0 for x < 0 . Idem C = 0 for x > 0.
    Why this is so is indeed not mentioned. So: how can they claim that ?
     
  4. Aug 12, 2017 #3
    I see it now, thank you for the insight!

    I assume that this is a possible solution arising out of the Schrodinger equation for a 1D finite well, and that C and D are adjusted to ensure that this wavefunction meets boundary conditions? Is this answer somewhat correct?
     
  5. Aug 12, 2017 #4

    BvU

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    The wavefunction has to be normalizable. That excludes terms ##e^{+x}## on the far right and ##e^{-x}## on the far left.
     
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