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Feb 23, 2013 at 0:31 comment added Michael The problem is that the $x$ and $y$ oscillators don't individually commute with $\hat{L}_z$, only their combination does. So you can't solve for them in terms of independent $n_x,\ n_y$ (there is some nontrivial constraint condition on the expansion coefficients).
Feb 22, 2013 at 16:21 history answered Rhys CC BY-SA 3.0