Friday, June 8, 2012

1206.1555 (D. Ojeda-Guillén et al.)

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

D. Ojeda-Guillén, R. D. Mota, V. D. Granados
From the definition of the standard Perelomov coherent states (PCS) we introduce the Perelomov number coherent states (PNCS) of the su(1,1) Lie algebra for any realization of its generators. The displacement operator allows to apply a similarity transformation to the su(1,1) generators and construct a set of operators which close the su(1,1) Lie algebra, being the PNCS the basis for its unitary irreducible representation. We evaluate the Schr\"odinger's uncertainty relationship (SUR) for a position and momentum-like operators (constructed from the Lie algebra generators) in the PNCS and show that it is minimized for the PCS. We obtain the time evolution of the PNCS and the algebra generators and prove that the SUR is minimized for t=0 and the PCS. Also, we obtain analogous results to these for the SU(2) PNCS. We emphasize that our treatment is strictly algebraic and does not depend on the explicit form of the PNCS, even we report those states.
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