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Homework Help: Degeneracy and orthogonality

  1. Nov 5, 2008 #1
    1. The problem statement, all variables and given/known data

    Are all electronis states orthonormal?
    I mean the degenerate states ie [n,l,m>states corresponding to same energy
    for example can one write
    [2,0,0>=a[2,1,-1>+b[2,1,0>+c[2,1,+1>

    2. Relevant equations



    3. The attempt at a solution

    for example can one write
    [2,0,0>=a[2,1,-1>+b[2,1,0>+c[2,1,+1>???
     
  2. jcsd
  3. Nov 6, 2008 #2
    [tex]<n',l',m'|n,l,m>=\delta_{n'n}\delta_{l'l}\delta_{m'm}[/tex]

    So you cannot write |2,0,0> as a superposition of the three l=1 states.
     
  4. Nov 6, 2008 #3
    Fine but how do you go about the proof???

    forget about in the wavemechanics
    just a general proof in bra-ket notation,showing that degenerate states are orthonormal.
     
  5. Nov 6, 2008 #4
    They are eigenstates of hermitian operators (namely, angular momentum) with different eigenvalues.
     
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