Continuity Equation in Presence of a Non-Local Potential in Non-Commutative Phase-Space

作     者：Ilyas Haouam 

作者机构：Laboratoire de Physique Mathematique et de Physique Subatomique(LPMPS)Universite Freres MentouriConstantineAlgeria 

出 版 物：《Open Journal of Microphysics》 (微观物理学期刊（英文）)

年 卷 期：2019年第9卷第3期

页      面：15-28页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Continuity Equation Non-Local Potential Non-Commutative Schrodinger Equation Phase-Space Non-Commutativity Frahn-Lemmer Potential Moyal Product Bopp-Shift Linear Transformation 

摘      要：We studied the continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore, we examined the influence of the phase-space non-commutativity on both the locality and the non-locality, where the definition of current density in commutative phase-space cannot satisfy the condition of current conservation, but with the steady state, in order to solve this problem, we give a new definition of the current density including the contribution due to the non-local potential. We showed that the calculated current based on the new definition of current density maintains the current. As well for the case when the non- commutativity in phase-space considered, we found that the conservation of the current density completely violated;and the non-commutativity is not suitable for describing the current density in presence of non-local and local potentials. Nevertheless, under some conditions, we modified the current density to solve this problem. Subsequently, as an application we studied the Frahn-Lemmer non-local potential, taking into account that the employed methods concerning the phase-space non-commutativity are both of Bopp-shift linear transformation through the Heisenberg-like commutation relations, and the Moyal-Weyl product.