TY - JOUR
AU - Maireche, A.
PY - 2020/11/12
Y2 - 2022/08/16
TI - 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
JF - Ukrainian Journal of Physics
JA - Ukr. J. Phys.
VL - 65
IS - 11
SE - General physics
DO - 10.15407/ujpe65.11.987
UR - https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2019498
SP - 987
AB - <p>Within the framework of nonrelativistic noncommutative quantum mechanics using the improved approximation scheme to the centrifugal term for any l-states via the generalized Bopp’s shift method and standard perturbation theory, we have obtained the energy eigenvalues of a newly proposed generalized Hellmann potential model (the GHP model) for the hydrogenic atoms and neutral atoms. The potential is a superposition of the attractive Coulomb potential plus Yukawa one, and new central terms appear as a result of the effects of noncommutativity properties of space and phase in the Hellmann potential model. The obtained energy eigen-values appear as a function of the generalized gamma function, the discrete atomic quantum numbers (j, n, l, s and m), infinitesimal parameters (a, b, б) which are induced by the position-position and phase-phase noncommutativity, and, the dimensional parameters (Θ, 0) of the GHP model, in the nonrelativistic noncommutative three-dimensional real space phase (NC: 3D-RSP). Furthermore, we have shown that the corresponding Hamiltonian operator with (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of the Hellmann potential model and two operators, the first one is the modified spin-orbit interaction, while the second is the modified Zeeman operator for the hydrogenic and neutral atoms.</p>
ER -