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What's the total angular momentum operator for a system of two particles?

  1. Aug 13, 2009 #1
    Suppose we're in two dimensions, and both particles have mass 1.

    Particle 1's location is given by its polar coordinates [itex](r_1,\theta_1)[/itex]; likewise for Particle 2 [itex](r_2,\theta_2)[/itex].

    Is it true that the total angular momentum [itex]\vec{L}[/itex] is just the sum of the individual angular momenta of the particles: [itex]\vec{L} = \vec{L}_1 + \vec{L}_2[/itex]? If that's the case, can you give me the total angular momentum operator [itex]\vec{L}[/itex] as a differential operator?
  2. jcsd
  3. Aug 13, 2009 #2
    yeah, just add it up: [tex] L_j^z = -i\hbar \left[y_j\partial/\partial{x_j} - {x_j}\partial/\partial{y_j}\right][/tex] where j is the particle index. Keep in mind L_2 does not act on the coordinates for the first particle.
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