On a dynamical symmetry group of the relativistic linear singular oscillator

Abstract

An exact approach for the factorization of the relativistic linear singular oscillator is proposed. This model is expressed by the finite-difference Schrödinger-like equation. We have found finite-difference raising and lowering operators, which are with the Hamiltonian operator form the close Lie algebra of the $SU(1,1)$ group.

7 pages, EPL style LaTeX file, accepted for publication in Europhysics Letters

References in corpus (6)

• Exchange Operator Formalism for Integrable Systems of Particles
• Spectrum of a spin chain with inverse square exchange
• Bound States of the Dirac Equation for a Class of Effective Quadratic Plus Inversely Quadratic Potentials
• Quantum singular oscillator as a model of two-ion trap: an amplification of transition probabilities due to small time variations of the binding potential
• The Relativistic Linear Singular Oscillator
• A relativistic model of the isotropic three-dimensional singular oscillator

Cited by in corpus (3)

• A relativistic model of the $N$-dimensional singular oscillator
• A set of nonlinear coherent states for the pseudoharmonic oscillator
• Polyanalytic relativistic second Bargmann transforms