2005/09/13 by Monique Combescure, Combescure, Monique, Didier Robert +1
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0509027
arxiv created 2005/09/13 · openalex publication_date 2005/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Time dependent quadratic Hamiltonians are well known as well in classical mechanics and in quantum mechanics. In particular for them the correspondance between classical and quantum mechanics is exact. But explicit formulas are non trivial (like the Mehler formula). Moreover, a good knowlege of quadratic Hamiltonians is very useful in the study of more general quantum Hamiltonians and associated Schrödinger equations in the semiclassical regime. Our goal here is to give our own presentation of this important subject. We put emphasis on computations with Gaussian coherent states. Our main motivation to do that is application concerning revivals and Loschmidt echo.