Quantum Mechanics on the h-deformed Quantum Plane

Details Quantum Mechanics on the h-deformed Quantum Plane Quantum Mechanics on the h-deformed Quantum Plane

1998-04-25

arxiv.org/abs/math-ph/9804015v3

J. phys. A, 32 (1999) 2091-2102

Physics

Mathematical Physics

16pages, Latex2e, Abstract and section 4 have been revised

Scientific paper

10.1088/0305-4470/32/11/005

We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami operator on the extended $h$-deformed quantum plane and solve the Schr\"odinger equations explicitly for some physical systems on the quantum plane. In the commutative limit the behaviour of a quantum particle on the quantum plane becomes that of the quantum particle on the Poincar\'e half-plane, a surface of constant negative Gaussian curvature. We show the bound state energy spectra for particles under specific potentials depend explicitly on the deformation parameter $h$. Moreover, it is shown that bound states can survive on the quantum plane in a limiting case where bound states on the Poincar\'e half-plane disappear.

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