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It is shown that each one of the Lie algebras su(1,1) and su(2) determine thespectrum of the radial oscillator. States that share the same orbital angularmomentum are used to construct the representation spaces of the non-compact Liegroup SU(1,1). In addition, three different forms of obtaining therepresentation spaces of the compact Lie group SU(2) are introduced, they arebased on the accidental degeneracies associated with the spherical symmetry ofthe system as well as on the selection rules that govern the transitionsbetween different energy levels. In all cases the corresponding generalizedcoherent states are constructed and the conditions to squeeze the involvedquadratures are analyzed.

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