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Angular momentum and coordinates

  1. Dec 16, 2012 #1
    let us denote the joint eigenstate of [itex]\hat{L^{2}}[/itex]and [itex]\hat{L_{z}}[/itex] by ll,m> and we know that if we are in spherical coordinates,
    [itex]\hat{L^{2}}[/itex] and [itex]\hat{L_{z}}[/itex] depend on θ and ∅, so we denote the joint eigenstate by: <θ∅l l,m>.. why?
     
    Last edited: Dec 16, 2012
  2. jcsd
  3. Dec 16, 2012 #2

    dextercioby

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    The bra-ket is a complex number, the value of the wavefunction (singled out by a choice of l and a choice of m) in terms of the spherical angles, i.e. coordinate variables.
     
  4. Dec 17, 2012 #3
    are you looking for simultaneous eigenstate.then L2 and Lz commute so that it is possible to find simultaneous eigenstates.
     
  5. Dec 17, 2012 #4
    We denote it that way because we've chosen to project the eigenstates and the operators in terms of [itex]\theta[/itex] and [itex]\phi[/itex]. We could equally express the eigenstates [itex]|l, m \rangle[/itex] and the operators [itex]\hat{L^{2}}[/itex] and [itex]\hat{L_{z}}[/itex] in terms of Cartesian coordinates. We express the eigenstates in the standard Cartesian basis as [itex]\langle x, y, z|l, m \rangle[/itex]. They aren't as pretty to work with, which is why we choose spherical coordinates to express spherical harmonics.
     
  6. Dec 26, 2012 #5
    Thanks jmcelve. It is clear now.
     
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