Deformed Heisenberg algebras, a Fock-space representation and the Calogero model
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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.
KeywordsQuantum Mechanic Harmonic Oscillator Leibniz Rule Heisenberg Algebra Ordinary Quantum
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