= Anisotropic quantum harmonic oscillator
{title2=$E_{n_xn_yn_z}=\hbar\sum_i\omega_i(n_i+1/2)$}
For a positive diagonal quadratic potential $V=m\sum_i\omega_i^2x_i^2/2$, coordinate <Hamiltonians> commute and <wavefunctions> separate into one-dimensional oscillator factors. Equality of two squared <frequencies> gives <rotation> <symmetry> in their plane; equality of all three gives full <rotation> <symmetry>. Equalities create <energy> degeneracies and extra conserved <angular momentum>. Merely finding an accidental equality between particular level energies does not establish a global <rotational symmetry>.
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