Physical review. A, General physics · 1985 · 172 citations · 15 references
Natural SciencesPhysicsDynamical SystemsOpticsQuantum MechanicsCanonical TransformationsHamiltonian SystemsNonlinear OpticsQuantum DynamicsCoherence DynamicsCoherent StatesHamiltonian FormulationHamiltonian Formulation Of General RelativityOptical Parametric OscillationOptical Parametric OscillatorsQuantum HamiltonianTime Evolution Of States
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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Coherent states for arbitrary Lie group
A. M. Perelomov · Communications in Mathematical Physics · 1972 · 1.3K citations · Full text
Irreducible Unitary Representations of the Lorentz Group
V. Bargmann · Annals of Mathematics · 1947 · 1.3K citations