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Spherical Harmonics/Angular Momentum

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data

    Given that Lz(x+iy)m=m[itex]\hbar[/itex](x+iy)m. Show that L+=(x+iy)m.

    2. The attempt at a solution

    I'm probably grasping at straws here, but when I see the expression for Lz I instantly go to Lz|lm>=m[itex]\hbar[/itex]|lm>. This then leads me to suspect that |lm>=(x+iy)m. Is this correct, and how on Earth does it get me any closer to what I want to show for the raising operator?
     
  2. jcsd
  3. Oct 23, 2011 #2

    vela

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    Not exactly. What [itex]\hat{L}_z(x+iy)^m=\hbar m(x+iy)^m[/itex] tells you is that [itex](x+iy)^m \propto \langle x,y | l~m \rangle[/itex]. You need to keep the distinction between kets and the representation of the ket in some basis. Writing [itex](x+iy)^m = |l~m\rangle[/itex] is, at best, a terrible abuse of notation.

    I have no idea what [itex]\hat{L}_+ = (x+iy)^m[/itex] is supposed to mean.
     
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