Coherent states for general potentials. IV. Three-dimensional systems

The minimum-uncertainty coherent-states formalism is extended to higher-dimensional systems. Specifically, for spherically symmetric three-dimensional potentials the formalism looks for coherent states which are products of an angular wave function times a radial wave function. After reviewing the many studies on angular coherent states, I concentrate on the physically distinguishing radial coherent states. The radial formalism is explained in detail and contrasted with the effective one-dimensional formalism. The natural classical variables in the radial formalism are those which vary sinusoidally as g(E,L)theta(t), where theta(t) is the real azimuthal angular variable and g(E,L) is the number of oscillations between apsidal distances per classical orbit. When changed to natural quantum operators, these operators can be given as the Hermitian sums and differences of the ''l'' raising and lowering operators. The formalism is applied to the three-dimensional harmonic-oscillator and Coulomb problems