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Unitary relation for the time-dependent SU(1,1) systems

Dae-Yup Song
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Abstract

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 Schrödinger 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).

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Dae-Yup Song. 2003-03-24. Unitary relation for the time-dependent SU(1,1) systems. https://doi.org/10.1103/physreva.68.012108

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