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Physics Letters A

The controllability of the pure states for the Morse potential with a dynamical group SU(1,1)

Shi‐Hai Dong, F. Lara-Rosano, Guo-Hua Sun

Published Apr 10, 2004• 8 citations
Publisher
DOI
10.1016/j.physleta.2004.03.061

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In a recent paper (Aldaya V and Guerrero J 2005 J. Phys. A: Math. Gen. 38 6939 ) it is shown that the bound states of the Modified Pöschl–Teller potential should be described by the non-compact dynamical group SU (1, 1) instead of the usual compact group SU (2). Here we prove that SU (2) cannot be the dynamical group for a potential with a finite number of bound states on the basis of the Modified Pöschl–Teller potential and the Morse potential. This suggests that a quantum system with a continuum spectrum and a finite number of bound states should be described, both in the continuum and the discrete spectrum, by a non-compact dynamical group instead of a compact one.