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QM: Potential Well

  1. Sep 28, 2008 #1
    1. The problem statement, all variables and given/known data

    An experimental physicist submits a proposal to a granting agency requesting support to construct an infinite potential well analogous to the one shown in Figure 3.5 (an electron trapped in a one dimensional box made of electrodes and grids in an evacuated tube). Specifically, the proposal is to build a well with L = 1mm, inject some electrons into it, and then measure the wavelength of photons emitted during low-n transitions via optical spectroscopy. As an expert on quantum mechanics, you are asked to evaluate the proposal. What is your recommendation?

    2. Relevant equations

    E = [tex]\frac{\pi^2\hbar^2}{2 m L^2}n^2[/tex]

    [tex]\lambda[/tex] = [tex]\frac{h c }{E}[/tex]

    3. The attempt at a solution

    Questions: Can electrons transition without a nucleus? Is it responding to some nucleus outside of the well? Does it have nothing to do with nuclei at all? What exactly are low-n transitions?

    I'm very confused, so any direction would be appreciated. I know that the proposal should be refused, but I don't know why. By playing around with the equations above, I though perhaps that the wavelength wasn't in the visual spectrum, but I'm not sure that combining the two equations even makes sense.
  2. jcsd
  3. Sep 29, 2008 #2


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    Homework Helper

    you can take "low-n transitions" to mean n=1 or 2 or so. That is, plug in n=1 or 2 or whatever to the 'E' formula and find E. Then plug that E into the '[itex]\lambda[/itex] formula and find [itex]\lambda[/itex]. Compare the wavelength you find to the wavelength of visible light.
  4. Sep 29, 2008 #3
    Thank you very much. That's what I did initially, but I wasn't sure if that was the right method.
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