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Particles and Fields
Eur. Phys. J. C 17, 539-547
DOI 10.1007/s100520000457

Deformed Heisenberg algebras, a Fock-space representation
and the Calogero model

V. Bardek - S. Meljanac

Theoretical Physics Division, Rudjer Boskovic Institute, P.O. Box 180, 10002 Zagreb, Croatia

Received: 27 April 2000 / Published online: 8 September 2000 - © Springer-Verlag 2000

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.

Copyright Società Italiana di Fisica, Springer-Verlag 2000