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 Schr\"odinger's uncertainty relationship is evaluated for a position and momentum-like operators (constructed from Lie algebra generators) in these It shown that this minimized standard obtain time evolution states by supposing Hamiltonian proportional to third generator $K_0$ $su(1,1)$ algebra. Analogous results $SU(2)$ are found. As examples, we compute pseudoharmonic oscillator two-dimensional isotropic harmonic oscillator.