Complex su_q(2) Dynamical Symmetry, Limiting Cases and 1-Dimensional Potential Realisation

Details Complex su_q(2) Dynamical Symmetry, Limiting Cases and 1-Dimensional Potential Realisation Complex su_q(2) Dynamical Symmetry, Limiting Cases and 1-Dimensional Potential Realisation

1996-12-04

arxiv.org/abs/q-alg/9612007v1

Mathematics

Quantum Algebra

37 pages, Latex, 8 figures, PACS: 03.65.Fd, 11.30.Na, Submitted J. Phys. A: Math. Gen

Scientific paper

Using a complex deformation q=exp(is) of su(2) we obtain extensions of the finite-dimensional representations towards the infinite-dimensional ones. A generalised q-deformation of su(2), as a Hopf algebra is introduced. We present the corresponding Schrodinger picture, by using a differential realisation, and a large class of potentials is obtained.A connection between the unirreps with q a root of unity and the comensurability of the potentials is investigated. The smooth transition between su(2) and su(1,1) , through E(1) is obtained at different levels: of the unirreps, of the topology, of the commutators and of the potentials in the corresponding Schrodinger equation.

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