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Quantum Physics help/Electron trap problem

  1. Dec 5, 2011 #1
    1. The problem statement, all variables and given/known data
    A rectangular corral of widths Lx = L and Ly = 1.94L contains seven electrons. What multiple of h2/8mL2 gives the energy of the ground state of this system? Assume that the electrons do not interact with one another, and do not neglect spin.


    2. Relevant equations
    Enx,ny = h^2/(8mL^2) (nx^2 + ny^2)



    3. The attempt at a solution
    used (nx/Lx)^2 + (ny/Ly)^2 to solve for the energy states resulting in
    ground state: 1.266
    1st excited: 2.063 (or 2.266?)
    2nd excited: 5.063

    I feel this approach is incorrect because the 1st excited state could have two possible energy states...

    obviously, after finding the states, I multiplied 2 electrons by ground, 4 by 1st, and 1 by second, but the sum jumps around the answer instead of giving me a correct answer.

    I'm new to the forum posting, but you guys are always a big help for me so thanks for any input ahead of time.
     
  2. jcsd
  3. Dec 5, 2011 #2
    state energy
    1,1 2
    1,2 5
    2,1 5
    2,2 8

    So won't the energy be 2*2 + 5*2 + 5*2 + 8*1 or 32 multiples?
     
  4. Dec 5, 2011 #3
    Yes, there will be 32 multiples, but that would be assuming a square electron trap...I'm not sure how to figure out the multiples based on the trap being rectangular.
     
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