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Quantum Mechanics - Question Regarding Eigenenergy

  1. Feb 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Consider an electron in a three-dimensional cubic box of side length Lz. The walls of the box are presumed to correspond to infinitely high potentials.

    2. Relevant equations

    En=((h2)/8MLz2)(n2) where n corresponds to the principal quantum numbers in their respective axes

    3. The attempt at a solution

    My only question is if the side lengths of the cubic box are all of length Lz, does that necessarily mean that all of the principal quantum numbers "n" can be written as nz also or are they all independent of the each other and of the side lengths? Thanks.
  2. jcsd
  3. Feb 6, 2010 #2


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    Homework Helper

    Each quantum number is independent. The fact that the side lengths are all the same only means that the energy spectrum (the set of allowed energies) is the same in all 3 dimensions. So for example, the fact that the side lengths are the same means that if nx = ny, then the same amount of energy is associated with the x dimension as with the y dimension. But there's no reason that the actual values of different quantum numbers need to be the same, even if the sets of possible values are the same.
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