title: Adiabatic theorem and generalized geometrical phase in the case of continuous spectra.
abstract: By defining "a virtual gap" for the continuous spectrum through the notion of eigendifferential (Weyl's packet) and using the differential projector operator, we present a rigorous demonstration and discussion of the quantum adiabatic theorem for systems having a nondegenerate continuous spectrum. An explicit formula for a generalized geometrical phase is derived in terms of the eigenstates of the Hamiltonian. Examples are given for illustration.
authors.affiliation: Lab PQSD, Faculté des Sciences, Université Ferhat Abbas de Sétif, Sétif 19000 Algeria.
authors.forename: M
authors.initials: M
authors.lastname: Maamache
authors.forename: Y
authors.initials: Y
authors.lastname: Saadi