We construct an abstract pseudodifferential calculus with operator-valued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case where the electronic Hamiltonian admits a local gap in its spectrum. In particular, we show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, we study the propagation of certain wave packets up to long time values of Ehrenfest order.
Born-Oppenheimer Reduction of Quantum Evolution of Molecules / A. Martinez; V. Sordoni. - In: SUURI KAISEKI KENKYUUJO KOUKYUUROKU. - ISSN 1880-2818. - STAMPA. - (2006), pp. 151-168. (Intervento presentato al convegno Spectral and Scattering Theory and Related Topics tenutosi a Kyoto nel 16-18/01/06).
Born-Oppenheimer Reduction of Quantum Evolution of Molecules
MARTINEZ, ANDRE' GEORGES;SORDONI, VANIA
2006
Abstract
We construct an abstract pseudodifferential calculus with operator-valued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case where the electronic Hamiltonian admits a local gap in its spectrum. In particular, we show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, we study the propagation of certain wave packets up to long time values of Ehrenfest order.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
