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Deformed Heisenberg algebras, a Fock-space representation and the Calogero model. (English) Zbl 1099.81510

Summary: We describe generally deformed Heisenberg algebras in one dimension. The condition for a generalized Leibniz rule is obtained and solved. We analyze conditions under which deformed quantum-mechanical problems have a Fock-space representation. One solution of these conditions leads to a q-deformed oscillator already studied by Lorek et al., and reduces to the harmonic oscillator only in the infinite-momentum frame. The other solution leads to the Calogero model in ordinary quantum mechanics, but reduces to the harmonic oscillator in the absence of deformation.

MSC:

81R15 Operator algebra methods applied to problems in quantum theory
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