New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms

Abstract

Keywords:The Vibrational-Rotational Structure of Supersingular plus Coulomb potential, noncommutative space and phase, star product and Boopp's shift method.Abstract. In this study, three-dimensional modified time-independent Schrödinger equation of modified vibrational-rotational structure of supersingular plus Coulomb (v.r.s.c) potential was solved using Boopp's shift method instead to apply star product, in the framework of both noncommutativity three dimensional real space and phase (NC: 3D-RSP). We have obtained the explicit energy eigenvalues for ground state and first excited state for interactions in one-electron atoms. Furthermore, the obtained corrections of energies are depended on infinitesimal parameterswhich are induced by position-position and momentum-momentum noncommutativity, respectively, in addition to the discreet atomic quantum numbers:and the angular momentum quantum number m . We have also shown that, the usual states in ordinary three dimensional spaces for ordinary vibrational-rotational structure of supersingular plus Coulomb potential are canceled and has been replaced by new degenerated   1 2 2  l sub-states in the extended new quantum symmetries of (NC: 3D-RSP).

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

“…which expresses the asymptotic nature of the strong interaction at short distances and the confinement forceproportional to ( ) ia − produced from the linear part for describing the interaction between light and heavy mesons at large distances.This physical behavior is quite similarto the Cornell potential [43][44] .It can also be said that the physical behavior of the studied potential, in ordinary nonrelativistic quantum mechanics, is similar to the trigonometric Rosen-Morse potential (suggested as a quark-antiquark interaction potential)which is as a function of distance r for the exact and approximate potential on the second page of the Ref. 6 .…”

Heavy-Light Mesons in the Symmetries of Extended Nonrelativistic Quark Model

“…in (NC-3D: RSP) symmetries as follows [30][31][32][33][34][35]: . Thus, the reduced Schrödinger equation (without star product) can be written as:…”

Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

“…In order to construct a 2D model of NMKP, the essential step is to rewrite the ordinary SE to the new following modified Schrödinger equation (MSE) which play a major role in (NC: 2D-RSP) symmetries [23][24][25][26][27][28][29][30][31][32][33][34]:…”