Quadratic Quantum Hamiltonians revisited

Abstract

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.

References in corpus (2)

• A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition
• Semiclassical trace formulae using coherent states

Cited by in corpus (7)

• Nonlinear coherent states and Ehrenfest time for Schrodinger equation
• Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials
• Magnetic operations: a little fuzzy physics?
• Stability of wave packet dynamics under perturbations
• Landau problem with a general time-dependent electric field
• Nonlinear dynamics of semiclassical coherent states in periodic potentials
• Squeezed Coherent States and a Semiclassical Propagator for the Schroedinger equation in Phase