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Problem about orthogonality

  1. Oct 31, 2011 #1
    Suppose psi1 and psi2 are eigenstates of observables O1 and O2

    Suppose Value of O1 of psi1 = value of O1 of psi2

    Therefore, <psi1|psi2>=1

    Suppose value of O2 of psi1<>value of O2 of psi2

    Therefore <psi1|psi2>=0

    Contradiction!how to explain
  2. jcsd
  3. Oct 31, 2011 #2


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    Science Advisor

    This is not correct. Eigenvalues can be degenerate; that is, there can be more than one eigenstate for a particular eigenvalue. Example: in hydrogen, the energy only depends on the quantum number n, and not on the angular-momentum quantum numbers l and m. Eigenstates with the same value of n (and hence the same energy eigenvalue), but different values of l or m, are orthogonal.
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