SU(1,1) and SU(2) Approaches to the Radial Oscillator: Generalized Coherent States and Squeezing of Variances

TL;DR

This paper explores how su(1,1) and su(2) Lie algebras describe the spectrum of the radial oscillator, constructing generalized coherent states and analyzing quadrature squeezing for these states.

Contribution

It introduces new methods to construct representation spaces of su(1,1) and su(2) for the radial oscillator, and develops generalized coherent states with squeezing analysis.

Findings

Representation spaces for su(1,1) and su(2) are constructed for the radial oscillator.

Generalized coherent states are formulated for both Lie algebras.

Conditions for quadrature squeezing in these states are analyzed.

Abstract

It is shown that each one of the Lie algebras su(1,1) and su(2) determine the spectrum of the radial oscillator. States that share the same orbital angular momentum are used to construct the representation spaces of the non-compact Lie group SU(1,1). In addition, three different forms of obtaining the representation spaces of the compact Lie group SU(2) are introduced, they are based on the accidental degeneracies associated with the spherical symmetry of the system as well as on the selection rules that govern the transitions between different energy levels. In all cases the corresponding generalized coherent states are constructed and the conditions to squeeze the involved quadratures are analyzed.