Explicit n-particle harmonic oscillator states in products of SU(1,1) representations

Abstract

In this paper, we present a simple algorithm for the explicit construction of [Formula: see text]-particle harmonic oscillator states simultaneously belonging to irreducible representations of [Formula: see text] (or [Formula: see text]) and [Formula: see text]. For degenerate representations, the construction can be done using generating functions or hyperspherical harmonics. The cases with [Formula: see text] and [Formula: see text] are investigated at greater length. The analysis is extended to nondegenerate states, although the states are not so easily obtained as in the degenerate case. Finally, we briefly touch on the [Formula: see text] structure of Bell states.