= Two-dimensional Coulomb bound state
{title2=$E=-\mu\kappa^2/[2\hbar^2(n_r+|m|+1/2)^2]$}
For motion confined to a plane but retaining <potential energy> $-\kappa/r$, separation in <polar coordinates> gives angular <wavefunctions> $e^{im\phi}$ with integer $m$. The regular radial factor behaves as $r^{|m|}$ at the origin. Removing this power and the decaying <exponential function> leaves an <Generalized Laguerre polynomial> differential equation. <polynomial> termination requires $N=n_r+|m|+1/2$, yielding the displayed <energy>. At fixed $q=n_r+|m|$, the spinless <quantum degeneracy> is $2q+1$. This is not the logarithmic potential of <electrostatics> formulated entirely in two spatial dimensions.
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