Related papers: Commutator Anomaly in Noncommutative Quantum Mecha…
The Aharonov-Bohm (AB) effect in non-commutative quantum mechanics (NCQM) is studied. First, by introducing a shift for the magnetic vector potential we give the Schr$\ddot{o}$dinger equations in the presence of a magnetic field on NC space…
The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schr$\ddot{o}$dinger equations on noncommutative(NC) space we obtain the Landau energy levels and the energy correction that is caused by…
The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension. Finally the map of Sch$\ddot{o}$dinger…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
After discussing the peculiarities of quantum systems on noncommutative (NC) spaces with non-trivial topology and the operator representation of the $\star$-product on them, we consider the Aharonov-Bohm and Casimir effects for such spaces.…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
Some ambiguities have recently been found in the definition of the partial derivative (in the case of presence of both explicit and implicit dependencies of the function subjected to differentiation). We investigate the possible influence…
This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in…
We introduce the perturbative aspects of noncommutative quantum mechanics. Then we study the Berry's phase in the framework of noncommutative quantum mechanics. The results show deviations from the usual quantum mechanics which depend on…
The dynamics of a spin--1/2 neutral particle possessing electric and magnetic dipole moments interacting with external electric and magnetic fields in noncommutative coordinates is obtained. Noncommutativity of space is interposed in terms…
We propose a model of dynamical noncommutative quantum mechanics in which the noncommutative strengths, describing the properties of the commutation relations of the coordinate and momenta, respectively, are arbitrary energy dependent…
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
In noncommutative space to maintain Bose-Einstein statistics for identical particles at the non-perturbation level described by deformed annihilation-creation operators when the state vector space of identical bosons is constructed by…
Recently, some problems have been found in the definition of the partial derivative in the case of the presence of both explicit and implicit functional dependencies in the classical analysis. In this talk we investigate the influence of…
Ambiguities have recently been found in the definition of the partial derivative (in the case of presence of both explicit and implicit dependencies of the function subjected to differentiation). We investigate the possible influence of…
We have studied particle motion in generalized forms of noncommutative phase space, that simulate monopole and other forms of Berry curvature, that can be identified as effective internal magnetic fields, in coordinate and momentum space.…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…