Graffi S., Unguendoli F.
Resonant Harmonic Oscillators and Eigenvalue Multiplicity
(40K, LaTeX)

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
$s=n-1$.