# Quantum mechanics on the h-deformed quantum plane

@article{Cho1998QuantumMO, title={Quantum mechanics on the h-deformed quantum plane}, author={Sunggoo Cho}, journal={Journal of Physics A}, year={1998}, volume={32}, pages={2091-2102} }

We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami operator on the extended h-deformed quantum plane and solve the Schrodinger 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 Poincare half-plane, a surface of constant negative Gaussian curvature. We show that the bound state energy spectra for particles under specific…

## 7 Citations

LAGRANGIAN AND HAMILTONIAN FORMALISM ON THE h-DEFORMED QUANTUM PLANE

- Mathematics
- 2000

It is known that there are only two quantum planes which are covariant under the quantum deformations of GL(2) admitting a central determinant. Contrary to the q-deformed quantum plane, the…

The fuzzy BTZ

- Mathematics
- 2022

We introduce a model of a noncommutative BTZ black hole, obtained by quantisation of Poincaré coordinates together with a moving frame. The fuzzy BTZ black hole carries a covariant diﬀerential…

FINITE FIELD THEORY ON NONCOMMUTATIVE GEOMETRIES

- Mathematics
- 1999

The propagator is calculated on a noncommutative version of the flat plane and the Lobachevsky plane with and without an extra (Euclidean) time parameter. In agreement with the general idea of…

Propagator on the h-deformed Lobachevsky plane

- Mathematics
- 2000

The action of the isometry algebra Uh (sl (2)) on the h -deformed Lobachevsky plane is found. The invariant distance and the invariant two-point functions are shown to agree precisely with the…

Properties of 2 × 2 h-Deformed Quantum (Super)Matrices

- Mathematics, Physics
- 2003

We investigate the h-deformed quantum (super)group of 2 × 2 matrices and use a kind of contraction procedure to prove that the n-th power of this deformed quantum (super)matrix is quantum…

Path integral solutions for deformed Pöschl–Teller-like and conditionally solvable potentials

- Physics, Mathematics
- 1999

I discuss in this paper the behaviour of the solutions of the so-called q-hyperbolic potentials, i.e. Poschl–Teller-like and conditionally solvable potentials, in terms of the path integral…

Noncommutative geometry for pedestrians

- Physics
- 1999

A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to…

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