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   ,   and   ,  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shown that, the usual states in ordinary three dimensional spaces for ordinary Kratzer potential are canceled and have been replaced by new degenerated 2(2l + 1) sub-states in the extended new quantum mechanics.

A New Relativistic Study for Interactions in One-electron atoms (Spin ½ Particles) with Modified Mie-type Potential

“…potential in (NC: 3D-RS) using the generalization Boopp's shift method to discover the new symmetries and a possibility to obtain another applications to this potential in different fields. This work based essentially on our previously works [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. The organization scheme of the study is given as follows: In next section, we briefly review the Dirac equation with Mie-type potential on based to Refs.…”

A New Nonrelativistic Atomic Energy Spectrum of Energy Dependent Potential for Heavy Quarkouniom in Noncommutative Spaces and Phases Symmetries

“…Furthermore, to gives a physical interpretation to the eq. (23), we apply the same strategy, which we have applied in our previous work [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]…”

A New Theoretical Study of Quantum Atomic Energy Spectra for Lowest Excited States of Central (PIHOIQ) Potential in Noncommutative Spaces and Phases Symmetries at Plan’s and Nanoscales

“…In this section, we shell give the deformed Hamiltonian operator nc sep H  for modified (CPIHOIQ) potential in (NC-2D: RSP), it satisfied by the following translations [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] r and 2 p in NC-2D: RSP , we can deduce that the roles  and  are oppositely and satisfied the symmetries of space-phase, furthermore the new operators ˆi…”

“…jl  (spin up) and 1 2 jl  (spin down), respectively [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]:…”

“…The parameters   and   are an antisymmetric real matrixes, the formalism of star product, Boopp's Shift method and the Seiberg-Witten map were played crucial roles in this new theory. The Boopp's shift method will be apply in present paper instead of solving the (NC-2D: RSP) with star product, the Schrödinger equation will be treated by using directly the following commutators [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]…”