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Energy eigenvalues and ground-state energy

  1. Sep 6, 2010 #1
    1. The problem statement, all variables and given/known data
    The energy eigenvalues of a particles of mass, m, confined to a 3-d cube of side a are:

    E[tex]_{nx,ny,nz}[/tex]=[tex]\frac{a(n^{2}_{x}+n^{2}_{y}+n^{2}_{z})}{b}[/tex]+ Vo

    where:
    a= planks constant^2(pi)^2
    b=2m^2
    nx,ny,nz = any positive integers.

    What are the ground-state kinetic and potential energies of the particle.


    3. The attempt at a solution
    Really stumped. Any hints would be helpful thanks.
     
  2. jcsd
  3. Sep 7, 2010 #2
    Try starting with the kinetic and potential energy operators.
     
  4. Sep 7, 2010 #3
    So
    Ke = 3a(n[tex]^{2}_{x}[/tex]) /b ?

    And Pe would be re-arranging to have Vo = E - 3a(n[tex]^{x}_{2}[/tex] )/b
     
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