SU (1, 1) and SU (2) Perelomov number coherent states: algebraic approach for general systems

We study some properties of the SU (1, 1) Perelomov number coherent states. The Schrödinger’s uncertainty relationship is evaluated for a position and momentum-like operators (constructed from the Lie algebra generators) in these number coherent states. It is shown that this relationship is minimized for the standard coherent states. We obtain the time evolution of the number coherent states by supposing that the Hamiltonian is proportional to the third generator K0 of the su(1, 1) Lie algebra. Analogous results for the SU (2) Perelomov number coherent states are found. As examples, we compute the Perelomov coherent states for the pseudoharmonic oscillator and the two-dimensional isotropic harmonic oscillator.