The number radial coherent states for the generalized MICZ-Kepler problem

TL;DR

This paper analyzes the radial MICZ-Kepler problem using $su(1,1)$ algebra, deriving energy spectra, eigenfunctions, and constructing coherent states with their time evolution.

Contribution

It introduces a novel algebraic approach to the MICZ-Kepler problem, constructing Perelomov number coherent states and analyzing their dynamics.

Findings

Derived the energy spectrum and eigenfunctions using $su(1,1)$ algebra.

Constructed Perelomov number coherent states for the problem.

Computed expectation values and time evolution of the coherent states.

Abstract

We study the radial part of the MICZ-Kepler problem in an algebraic way by using the $su(1,1)$ Lie algebra. We obtain the energy spectrum and the eigenfunctions of this problem from the $su(1,1)$ theory of unitary representations and the tilting transformation to the stationary Schr\"odinger equation. We construct the physical Perelomov number coherent states for this problem and compute some expectation values. Also, we obtain the time evolution of these coherent states.