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A mathematical introduction to the Wigner formulation of quantum mechanics

Luigi Barletti (2003)

Bollettino dell'Unione Matematica Italiana

The paper is devoted to review, from a mathematical point of view, some fundamental aspects of the Wigner formulation of quantum mechanics. Starting from the axioms of quantum mechanics and of quantum statistics, we justify the introduction of the Wigner transform and eventually deduce the Wigner equation.

absence de résonance près du réel pour l’opérateur de Schrödinger

Nicolas Burq (1997/1998)

Séminaire Équations aux dérivées partielles

On donne dans cet exposé des bornes inférieures universelles, en limite semiclassique, de la hauteur des résonances de forme associées aux opérateurs de Schrödinger à l’extérieur d’obstacles avec des conditions au bord de Dirichlet ou de Neumann et des potentiels analytiquement dilatables et tendant vers 0 à l’infini. Ces bornes inférieures sont exponentiellement petites par rapport à la constante de Planck.

Abstract quasi-variational inequalities of elliptic type and applications

Yusuke Murase (2009)

Banach Center Publications

A class of quasi-variational inequalities (QVI) of elliptic type is studied in reflexive Banach spaces. The concept of QVI was earlier introduced by A. Bensoussan and J.-L. Lions [2] and its general theory has been developed by many mathematicians, for instance, see [6, 7, 9, 13] and a monograph [1]. In this paper we give a generalization of the existence theorem established in [14]. In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators...

Canonical commutation relations and interacting Fock spaces

Zied Ammari (2004)

Journées Équations aux dérivées partielles

We introduce by means of reproducing kernel theory and decomposition in orthogonal polynomials canonical correspondences between an interacting Fock space a reproducing kernel Hilbert space and a square integrable functions space w.r.t. a cylindrical measure. Using this correspondences we investigate the structure of the infinite dimensional canonical commutation relations. In particular we construct test functions spaces, distributions spaces and a quantization map which generalized the work of...

Charge transfer scatteringin a constant electric field

Lech Zieliński (1999)

Colloquium Mathematicae

We prove the asymptotic completeness of the quantum scattering for a Stark Hamiltonian with a time dependent interaction potential, created by N classical particles moving in a constant electric field.

Circular operators related to some quantum observables

Wacław Szymański (1997)

Annales Polonici Mathematici

Circular operators related to the operator of multiplication by a homomorphism of a locally compact abelian group and its restrictions are completely characterized. As particular cases descriptions of circular operators related to various quantum observables are given.

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