Unitary relation for the time-dependent SU(1,1) systems
摘要
The system whose Hamiltonian is a linear combination of the generators of SU(1,1) group with time-dependent coefficients is studied. It is shown that there is a unitary relation between the system and a system whose Hamiltonian is simply proportional to the generator of the compact subgroup of the SU(1,1). The unitary relation is described by the classical solutions of a time-dependent (harmonic) oscillator. Making use of the relation, the wave functions satisfying the Schr\"{o}dinger equation are given for a general unitary representation in terms of the matrix elements of a finite group transformation (Bargmann function). The wave functions of the harmonic oscillator with an inverse-square potential is studied in detail, and it is shown that, through an integral, the model provides a way of deriving the Bargmann function for the representation of positive discrete series of the SU(1,1).
引用
@article{arxiv.quant-ph/0303143,
title = {Unitary relation for the time-dependent SU(1,1) systems},
author = {Dae-Yup Song},
journal= {arXiv preprint arXiv:quant-ph/0303143},
year = {2007}
}