94-65 Graffi S., Unguendoli F.

Resonant Harmonic Oscillators and Eigenvalue Multiplicity (40K, LaTeX) Mar 16, 94

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Abstract. Explicit formulas are worked out for the eigenvalue multiplicity of a system of $n$ independent quantum harmonic oscillators in the general case of $1\leq s\leq n-1$ resonance relations among the frequencies $\om_1,\ldots,\om_n$. As a particular case we prove that, even though the quantum numbers are always less than the degrees of freedom, the \ev s are in general intrinsically degenerate only in the completely resonant case $s=n-1$.

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