We derive the most general Hamiltonian which preserves the Perelomov SU(1,1) coherent states under time evolution. It is shown that the Hamiltonian of the degenerate parametric oscillator from nonlinear optics, which does not preserve ordinary coherent states, does preserve the SU(1,1) coherent states under time evolution.
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Christopher C. Gerry (1985) studied this question.
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