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Resonant harmonic oscillators and eigenvalue multiplicity

S Graffi and F Unguendoli

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Explicit formulae are worked out for the eigenvalue multiplicity of a system of n independent quantum harmonic oscillators in the general case of 1<or=s<or=n-1 resonance relations among the frequencies omega 1... omega n. As a particular case we prove that, even though the quantum numbers are always less than the degrees of freedom, the eigenvalues are, in general, intrinsically degenerate only in the completely resonant case s=n-1.


PACS

03.65.Ge Solutions of wave equations: bound states

02.10.Ud Linear algebra

MSC

15A90 Applications of matrix theory to physics

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 12 (21 June 1994)



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