Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Avodyne

    User Avatar
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Problem about orthogonality
Loading...