SU(1,1) coherent states defined via a minimum-uncertainty product and an equality of quadrature variances

Abstract

The coherent states of a Hamiltonian linear in SU(1,1) operators are constructed by defining them, in analogy with the harmonic-oscillator coherent states, as the minimum-uncertainty states with equal variance in two observables. The proposed approach is thus based on a physical characteristic of the harmonic-oscillator coherent states which is in contrast with the existing ones which rely on the generalization of the mathematical methods used for constructing the harmonic-oscillator coherent states. The set of states obtained by following the proposed method contains not only the known SU(1,1) coherent states but also a different class of states.