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Degeneracy of Energy Level

  1. Oct 25, 2013 #1
    Question
    Particle in a box (2D)
    Determine the energy levels (degeneracy) of the lowest three


    I found that E = A (4a^2 + b^2)
    where A is a constant
    a and b are positive integers (principle quantum number)


    My steps
    I assume 4a^2 + b^2 = k
    where k is also a positive integer

    The minimum value of a and b are 1, so k ≥ 5

    I would like to find the combination of a and b for a given k.
    But I don't know how to solve integral solution.

    Is there any systematic methods apart from trial and error ?
     
  2. jcsd
  3. Oct 25, 2013 #2

    DrClaude

    User Avatar

    Staff: Mentor

    Not trial and error, but a systematic exploration of all possibilities is quite easy here. Since the problem asks for the three lowest levels, ##b \le3## and you need only calculate a few values.
     
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