Abstract.
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.
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Received: 27 April 2000 / Published online: 8 September 2000
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Bardek, V., Meljanac, S. Deformed Heisenberg algebras, a Fock-space representation and the Calogero model. Eur. Phys. J. C 17, 539–547 (2000). https://doi.org/10.1007/s100520000457
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DOI: https://doi.org/10.1007/s100520000457