New Non-relativistic Bound States Solutions for Modified Kratzer Potential in One-electron Atoms

Abstract

In this study, three-dimensional modified time-independent Schrödinger equation of modified Kratzer potential was solved using Bopp’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 and first excited states for interactions in one-electron atoms. Furthermore, the obtained corrections of energies are depended on infinitesimal parameters ( ʘ,χ ) and ( θ, σ ) which are induced by position-position and momentum-momentum noncommutativity, respectively, in addition to the discreet atomic quantum numbers (j = l ± 1/2, s = 1/2, l and m). We have also shown that, the usual states in ordinary three dimensional spaces for ordinary Kratzer potential are canceled and have been replaced by new degenerated 2(2l + 1) sub-states in the extended new quantum mechanics.