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Cubo Mathematical Journal 8 (2006) 61-66

Quadratic Quantum Hamiltonians revisited

Monique Combescure1, Didier Robert2

(2006)

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.

1 :	IPNL - Institut de Physique Nucléaire de Lyon
2 :	LMJL - Laboratoire de Mathématiques Jean Leray

Domaine

:

Physique/Physique mathématique Mathématiques/Physique mathématique

Mots Clés : quadratic Hamiltonians – quantum mechanics – metaplectic representation – coherent states – Weyl quantization

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Contributeur : Didier Robert <>

Soumis le : Mardi 13 Septembre 2005, 15:28:40

Dernière modification le : Jeudi 23 Novembre 2006, 09:10:41