1995/11/13 by Jung Kon Kim, Sang Pyo Kim
Physics and Astronomy · #quant-ph
published as J.Korean Phys.Soc. 28 (1995) 7 · 22 pages of Latex file
arxiv created 1995/11/13 · arxiv updated 2009/12/01
For a time-dependent harmonic oscillator with an inverse squared singular term, we find the generalized invariant using the Lie algebra of SU(2) and construct the number-type eigenstates and the coherent states using the spectrum-generating Lie algebra of SU(1,1). We obtain the evolution operator in both of the Lie algebras. The number-type eigenstates and the coherent states are constructed group-theoretically for both the time-independent and the time-dependent harmonic oscillators with the singular term. It is shown that the squeeze operator transforms unitarily the time-dependent basis of the spectrum-generating Lie algebra of SU(1,1) for the generalized invariant, and thereby evolves the initial vacuum into a final coherent vacuum.