DOI 10.1007/s100520000457
Deformed Heisenberg algebras, a Fock-space representation
and the Calogero model
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
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.
Copyright Società Italiana di Fisica, Springer-Verlag 2000
