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Electron in a well: energies are quantized or not?

  1. Jan 27, 2008 #1
    hi, I'm new on this forum, and I don't know english very well (sorry). maybe you can clarify me about this doubt. an electron in a well with infinite walls has a discrete set of energies, right? but if the lenght of the well is infinite, what can I say about energy state density? is it uniform (as energy state density of a free electron: that's reasonable, as a well of infinite lenght should simulate this situation), or not? calculus seems to avvalorate this second hypothesis...
     
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  3. Jan 27, 2008 #2

    Dr Transport

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    A finite well will have a finite number of allowed states associated with it and the energy density will be a series of delta functions.
     
  4. Jan 27, 2008 #3
    right, but in an infinite well such series becomes a continous energy density because energy levels addensate: try to imagine...
     
  5. Jan 27, 2008 #4

    jtbell

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    addensate? :confused:
     
  6. Jan 27, 2008 #5

    Dr Transport

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    The infinite well never has a continuous series of energy states, only discrete states..

    I'm with jtbell, "addensate"????
     
  7. Jan 27, 2008 #6

    jtbell

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    I think he's referring to an infinitely wide well, not an infinitely deep one.
     
  8. Jan 27, 2008 #7

    Ben Niehoff

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    From the Latin roots, "addensate" should mean "to make more dense". Is your first language Italian, by any chance?
     
  9. Jan 28, 2008 #8
    yes, addensate=to make more dense! sorry, I thought this word exist in English. I'm referring to an infinitely wide well, not necessarily infinitely deep one: this should represent the free space. the question is: why energies in this case aren't distributed uniformly? for example, in a 3D-infinitely deep well energy density is an increasing function (right, energy states doesn't form a continous set, but a dense set not uniformly distributed when width is infinite)
     
    Last edited: Jan 28, 2008
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