Parameters of noncommutativity in Lie-algebraic noncommutative space

Abstract

We find condition on the parameters of noncommutativity on which a list of important results can be obtained in a space with Lie-algebraic noncommutativity. Namely, we show that the weak equivalence principle is recovered in the space, the Poisson brackets for coordinates and momenta of the center-of-mass of a composite system do not depend on its composition and reproduce relations of noncommutative algebra for coordinates and momenta of individual particles if parameters of noncommutativity corresponding to a particle are proportional inversely to its mass. In addition in particular case of Liealgebraic noncommutativity (space coordinates commute to time) on this condition the motion of the center-of-mass is independent of the relative motion and problem of motion of the center-of-mass and problem corresponding to the internal motion can be studied separately.

A New Approach to the Approximate Analytic Solution of the Three-Dimensional Schrӧdinger Equation for Hydrogenic and Neutral Atoms in the Generalized Hellmann Potential Model

“…It is clear that the obtained eigenvalues of energies are real, which allow us to consider the NC diagonal Hamiltonian ℎ (︀ , Θ, , )︀ as a Hermitian operator. In addition with regard for results (20), (22), and (47), the global Hamiltonian operator in the first order in and within the GHP model for hydrogenic atoms for ( , ) states takes the form:…”

“…The Bopp's shift method employed in the solutions enables us to explore an effective way of obtaining the modified potential in NRNCQM. It is based on the following commutators (see, e.g., [22][23][24][25][26][27]):…”

“…Edet et al studied bound-state solutions of the Schrödinger equation for the modified Kratzer potential plus screened Coulomb potential [16]. In this work, motivated by several recent studies such as the non-renormalizable of the standard model, string theory, quantum gravity, the noncommutative quantum mechanics (NCQM) has attracted much attention (see, e.g., [17][18][19][20][21][22][23]). Recently, we are studied the KGE with modified Coulomb potential plus inverse-square-root potential and modified Coulomb plus inverse-square potential in the noncommutative three-dimensional space [18,19].…”

“…(1)) used in the present study was first proposed by Edet et al [8]. The structure of nonrelativistic noncommutative quantum mechanics (NRNCQM) based to NC canonical commutations relations in the Schrödinger, Heisenberg, and interaction pictures (SP, HP, and IP), respectively, as follows (throughout this paper, the natural units = = 1 will be used) (see, e.g., [20][21][22][23][24][25][26][27]):…”

Solutions of Klein-Gordon equation for the modified central complex potential in the symmetries of noncommutative quantum mechanics

“…in relativistic threedimensional noncommutative quantum mechanicssymmetries [30][31][32][33][34][35][36][37][38][39][40][41][42] :…”