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Electron in an infinite well

  1. Nov 18, 2012 #1
    An electron is trapped in an infinite one-dimensional well of width 0.251nm. Initially the electron occupies the n=4 state. Suppose the electron jumps to the ground state with the accompanying emission of a photon. What is the energy of the photon?

    (Time independent)

    What I did was realize that [itex]\psi(x)[/itex] must equal zero at the walls, so I chose [itex]\sin(kL)[/itex] and set it to [itex]n\pi[/itex], then solved for k.

    Putting this value of k into the energy for a free particle (Time-ind Schrodinger), I eventually come to the expression:
    [tex]
    \frac{h^2 n^2}{8mL^2}
    [/tex]

    To find the corresponding energy of the emitted photon I plugged in the appropriate values of n and solved for the difference.

    Does that seem right?

    Answer:
    [tex]
    E=\frac{h^2 15}{8m L^2}
    [/tex]

    Obviously plugging in appropriate values of m and L afterward.
     
  2. jcsd
  3. Nov 18, 2012 #2

    Simon Bridge

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    That is certainly the method.
    If this is long answer you want to write it explicitly in the math though.
     
  4. Nov 18, 2012 #3
    Yeah, I have it officially written out showing steps and whatnot. Just felt lazy with the LaTex so I shortened it. Thanks.
     
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