$SU(1,1)$ coherent states for Dirac-Kepler-Coulomb problem in $D+1$ dimensions with scalar and vector potentials

Abstract

We decouple the Dirac's radial equations in $D+1$ dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an $su(1,1)$ algebra realization. Based on the theory of irreducible representations, we find the energy spectrum and the radial eigenfunctions. We construct the Perelomov coherent states for the Sturmian basis, which is the basis for the unitary irreducible representation of the $su(1,1)$ Lie algebra. The physical radial coherent states for our problem are obtained by applying the inverse original transformations to the Sturmian coherent states.

References in corpus (3)

• su(1,1) Algebraic approach of the Dirac equation with Coulomb-type scalar and vector potentials in D + 1 dimensions
• The Biedenharn Approach to Relativistic Coulomb-type Problems
• On the supersymmetry of the Dirac-Kepler problem plus a Coulomb-type scalar potential in D+1 dimensions and the generalized Lippmann-Johnson operator

Cited by in corpus (2)

• Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime
• Coherent states for the two-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field