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Homework Help: Conditions for quantised or continuous energies

  1. Apr 11, 2008 #1
    1. The problem statement, all variables and given/known data

    For a particle moving in a potential V(x), what are plausible forms of V(x) that give:

    (i) entirely continuous,

    (ii)entirely quantised

    (iii) both continuous and quantised

    energies of the particle? Sketch, with justification, the forms of V(x) for each of these 3 cases.

    2. Relevant equations

    3. The attempt at a solution

    (i) when the particle is free (V(x) is zero), the particles energies are continuous.

    (ii) When the particle is in an infinite potential well, the energies are quantised.

    (iii) I have no idea about this one. Can anyone help?
  2. jcsd
  3. Apr 11, 2008 #2


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    How about a square well whose sides have finite potential instead of infinite? Can you explain why that would work?
  4. Apr 11, 2008 #3
    So it would have quantised energy inside the well (since it's confined) and continuous energies outside the well?
  5. Apr 11, 2008 #4


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    If you mean by 'in' that it has energy less than the wall energy, yes.
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