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Quantum Mechanics on the h-deformed Quantum Plane

Sunggoo Cho
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Abstract

We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami operator on the extended $h$-deformed quantum plane and solve the Schrödinger 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 Poincaré 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 Poincaré half-plane disappear.

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Sunggoo Cho. 1999-03-30. Quantum Mechanics on the h-deformed Quantum Plane. https://doi.org/10.1088/0305-4470%2F32%2F11%2F005

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