Développement et traitement de certains problèmes de mécanique quantique

Abstract

The Schrödinger equation in interaction with local and non-local potentials in non commutative phase-space has been studied, the corresponding continuity equation has also been extracted in both types of phase-space, where, it has been found that the non-commutativity is not suitable for describing the current density, where this current density has been modi- ed to solve this problem. Also the Klein-Gordon, Dirac, DKP and Fisk-Tait equations have been studied in non-commutative phase space, where the Dirac equation in non-commutative time-dependent phase-space has been solved through the Lewis-Riesenfeld invariant method, and for the Fisk-Tait equation, it has been found that non-commutativity does not make the total charge obtained from the probability density de ned, in addition the correspondence between fermions and bosons in the Fock space has been shown using the Holstein-Primako representation. The non-relativistic limit of the Dirac and DKP equations in interaction with an electromagnetic eld in non-commutative phase-space was examined, the e ect of the noncommutativity on the non-relativistic limit was made according to two methods , the method of transformation of Foldy-Wouthuysen and approach of the big and small components of the wave function, these led to obtain the non-commutative non-relativistic equation of Schrödinger-Pauli.