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Questions about the projection operator

  1. Sep 1, 2004 #1
    A problem on my quantum homework assignment this week has to do with the projection operator P = |a><a|

    I've been asked to show that P^2=P, and then give the eigenvalues of P and then to characterize its eigenvectors. The first part is easy enough:

    P = |a><a|
    so P^2 = |a><a||a><a| = |a><a|a><a| = |a>(1)<a| = |a><a| = P

    It's the second part I'm having trouble with:

    P|psi> = p|psi> where little p is the eigenvalue.

    and coming the eigenvectors. Can anyone offer me a little help?
     
  2. jcsd
  3. Sep 1, 2004 #2

    robphy

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    Hint: Since P^2 v = P v, we have (P^2 - P) v =0.
     
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