Explicit formulas are worked out for the eigenvalue multiplicity of a systemof $n$ independent quantum harmonic oscillators in the general case of $1\leq s\leqn-1$ resonance relations among the frequencies$\om_1,\ldots,\om_n$. As a particular case we prove that, even though the quantumnumbers are always less than the degrees of freedom, the \ev s are in generalintrinsically degenerate only in the completely resonant case$s=n-1$.
Resonant harmonic oscillators and eigenvalue multiplicity / S., Graffi; Unguendoli, Francesco. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - STAMPA. - 27:(1994), pp. 4281-4293.
Resonant harmonic oscillators and eigenvalue multiplicity
UNGUENDOLI, Francesco
1994
Abstract
Explicit formulas are worked out for the eigenvalue multiplicity of a systemof $n$ independent quantum harmonic oscillators in the general case of $1\leq s\leqn-1$ resonance relations among the frequencies$\om_1,\ldots,\om_n$. As a particular case we prove that, even though the quantumnumbers are always less than the degrees of freedom, the \ev s are in generalintrinsically degenerate only in the completely resonant case$s=n-1$.Pubblicazioni consigliate
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