Any L-States Solutions of The Modified Schrodinger Equation with Generalized Hellmann-Kratzer Potential Model in The Symmetries of NRNCQM


Abdelmadjid Maireche

In the present research paper, the approximate analytical solutions of the modified radial Schrodinger equation (MSE) have been obtained with a newly proposed potential called generalized Hellmann–Kratzer potential (GHKP) model by using the improved approximation scheme to the centrifugal term for any l-states. The potential is a superposition of the Hellmann–Kratzer potential model and new terms proportional with (1/ r3, 1/ r4,  exp (-ar)/r2 and exp (-ar)/r3), appears as a result of the effects of noncommutativity properties of space and phase on the Hellmann–Kratzer potential model. We applied the generalized Bopp’s shift method and standard perturbation theory, in the nonrelativistic noncommutative three-dimensional real space phase (NC: 3D-RSP) instead to solving MSE directly with star product. The bound state energy eigenvalues for the some diatomic molecules such as, N2, CO, NO and CH  and obtained in terms of the generalized the Gamma function, the discreet atomic quantum numbers ((j, n, l, s, and m)), two infinitesimal parameters(a, b) which are induced automatically by position-position and phase-phase noncommutativity properties, in addition to, the dimensional parameters (V1, V, a, re, De) of GHKP model. Furthermore, we have shown that the corresponding Hamiltonian operator in (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of the HKP model and two operators, the first one is the modified spin-orbit interaction while the second is the modified Zeeman operator for the previous diatomic molecule.


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