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Raising and Lowering momentum operators

  1. Jan 4, 2009 #1
    [​IMG]

    I tried to use the eigenvalue of the operators but I couldn't get the result.
    Can anyone help me to understand this relationship?

    Thank you.
     
  2. jcsd
  3. Jan 5, 2009 #2
    if you multiply out the brackets inside the square root, you will find that they are in fact the eigenvalues of the L+ and L- operators.

    Remember that L+|l,m2> = Eigenvalue*|l,m2+1>

    Once you have operated with L+ on the left hand side you can move the eigenvalue out to the front as it is just a number. You are left with:

    <l,m1|l,m2+1>, which, by orthogonality, is 0 unless m1 = m2+1. This is precisely what the dirac delta functions on the right hand side represent.
     
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