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Angular momentum operators

  1. Oct 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Obtain the angular momentum operators [itex] L_{x} [/itex] and [itex] L_{y} [/itex] in the basis of functions [itex] Y^{\pm1}_{1}(\theta,phi}[/itex] and [tex] Y^{0}_{1}(\theta,phi}[/itex] in Lz representation

    2. The attempt at a solution
    To calculate the matrices for the Lx and Ly operators, do i simply have to take the relevant spherical harmonics and apply Lx and Ly like this

    To form the Lx the terms are given for n'n term of the matrix

    [tex] (L_{x})_{n'n} = <\psi^{(n'-2)}_{1}|L_{x}|\psi^{(n-2)}_{1}>[/tex]

    from this i can determine the terms of the Lx matrix
    similarly for the Ly matrix?

    am i correct? Thanks for any help.
  2. jcsd
  3. Oct 31, 2007 #2

    Meir Achuz

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    It's easier to use the raising and lowering operators L+ and L-.
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