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Question about finding quantom numbers N_(n) for Schrodinger Eqn in 3D

  1. Nov 25, 2013 #1
    I'm using the Modern Physics by Tipler (6th edition) book.
    In sec 7.1 it talks about the first excited state being either E_(112 ) E_(121 ) E_(112).

    My question is what is the process of finding the n_(1),n_(2),n_(3) quantum numbers ? How i understand you pick random values and from their find the order of energy levels. Can you give the process if would take of finding lets say the 4th excited state for both a cubic and non cubic box.

    Thank you for your time.

    PS: I apologize if my format is incorrect this is my fist post. The "_" represent subscript.
     
  2. jcsd
  3. Nov 28, 2013 #2
    Well, if the energy dependence on the quantum numbers were somehow more complicated, you could for example calculate the gradient to find some minimum values, and go from there. In this case, the minimum is trivially at 1,1,1. After you have that sorted, then all you can really do is calculate the energies for nearby quantum numbers. So you'd find E111, E112, ... , E122, E212, and so on. Then you just arrange the states according to their energy.
     
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