Bardek, V.; Meljanac, S. Deformed Heisenberg algebras, a Fock-space representation and the Calogero model. (English) Zbl 1099.81510 Eur. Phys. J. C, Part. Fields 17, No. 3, 539-547 (2000). 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. Cited in 11 Documents MSC: 81R15 Operator algebra methods applied to problems in quantum theory Keywords:Fock-space representation; Calogero model; 1D deformed Heisenberg algebras; Leibniz rule; deformed quantum-mechanics; q-deformed oscillator; harmonic oscillator; infinite-momentum frame; many body problem; deformed quantum mechanics PDFBibTeX XMLCite \textit{V. Bardek} and \textit{S. Meljanac}, Eur. Phys. J. C, Part. Fields 17, No. 3, 539--547 (2000; Zbl 1099.81510) Full Text: DOI arXiv