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Physics Letters A

On the controllability of a quantum system for the Morse potential with a compact group SU(2)

Shi‐Hai Dong, Yu Tang, Guo-Hua Sun

Published Dec 1, 2003• 24 citations
Publisher
DOI
10.1016/j.physleta.2003.11.022

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Using operators of the invariance group of their time-dependent Schr\"odinger equations it is shown that the bound states of Morse oscillators are bases for discrete nonunitary irreducible representations (non-UIRs) of the groups Sp(2,R)\mathrm{Sp}(2, R)Sp(2,R), SU(1,1), and SO(2,1). Hermiticity requirements and the dependence of the group generators on the dynamical variables determine the operator of an isometry which connects these non-UIRs of the noncompact invariance groups to UIRs of the compact groups SU(2) and SO(3) that have been used as spectrum-generating groups for Morse systems.