$SU(1,1)$ solution for the Dunkl oscillator in two dimensions and its coherent states

Abstract

We study the Dunkl oscillator in two dimensions by the $su(1,1)$ algebraic method. We apply the Schrödinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the $su(1,1)$ Lie algebra generators. The energy spectrum is found by using the theory of unitary irreducible representations. By solving analytically the Schrödinger equation, we construct the Sturmian basis for the unitary irreducible representations of the $su(1,1)$ Lie algebra. We construct the $SU(1,1)$ Perelomov radial coherent states for this problem and compute their time evolution.

14 pages

References in corpus (3)

• The su(1,1) dynamical algebra from the Schrödinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator
• SUSY QM, symmetries and spectrum generating algebras for two-dimensional systems
• Coherent states for the two-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field

Cited by in corpus (4)

• The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
• Spectral and Thermal Analysis of the Morse Potential within the Dunkl Formalism: Analytical Approximations and Applications