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Journal of the Korean Physical Society

Relativistic Treatment of Spin-zero Particles Subjected to the Shifted Tietz-Wei Potential Model

C. A. Onate, A. N. Ikot, M. C. Onyeaju, Eno E. Ituen, E. Aghemenloh, O. Ebomwonyi

Published Sep 1, 2018• 3 citations
Publisher

Abstract

The approximate solutions of the Klein-Gordon equation with the shifted Tietz-Wei potential function are thoroughly studied for Klein-Gordon equation with both 2 V and V potentials by using a suitable approximation scheme for the centrifugal term in the framework of the supersymmetric approach. The non-relativistic limits in both cases are obtained, and the numerical results are computed. We have equally investigated the Fisher information on the shifted Tietz-Wei potential function in the case of the non-relativistic limit of the Klein-Gordon equation with potential V because this is only possible in the non-relativistic regime. The Fisher information is observed to be inversely proportional to both C h and b h , where C h is the optimization parameter and b h = β (1 − C h ), with β being the Morse constant.

DOI
10.3938/jkps.73.531

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The approximate solutions of the Klein-Gordon equation with the shifted Tietz-Wei potential function are thoroughly studied for Klein-Gordon equation with both 2 V and V potentials by using a suitable approximation scheme for the centrifugal term in the framework of the supersymmetric approach. The non-relativistic limits in both cases are obtained, and the numerical results are computed. We have equally investigated the Fisher information on the shifted Tietz-Wei potential function in the case of the non-relativistic limit of the Klein-Gordon equation with potential V because this is only possible in the non-relativistic regime. The Fisher information is observed to be inversely proportional to both C h and b h , where C h is the optimization parameter and b h = β (1 − C h ), with β being the Morse constant.
Quantum relativistic solutions for a particle in a one-dimensional Morse potential are presented using methods previously proposed and applied to a particle in a harmonic oscillator. The methods lead to both numerical and analytical solutions, with the latter allowing smooth variation of the system parameters from non-relativistic to ultrarelativistic limits. Analytical expressions for the energy levels and wavefunctions are obtained, as solutions to a Schrödinger-type equation, including relativistic effects through a state dependent rescaled mass. The eigenstates of the Morse potential exhibit suitable and smooth behavior, and approach the corresponding harmonic oscillator solutions as the depth of the Morse potential well increases, as expected. A comparison is also presented between the relativistic harmonic oscillator obtained with this method, and the so-called Klein-Gordon oscillator.
In this research work, within the framework of relativistic and nonrelativistic noncommutative quantum mechanics, the deformed Klein–Gordon and Schrödinger equations were solved with the modified equal vector scalar Manning-Rosen potential that has been of significance interest in recent years using Bopp's shift method and standard perturbation theory in the first-order in the noncommutativity parameters in 3-dimensions noncommutative quantum mechanics. By employing the improved approximation of the centrifugal term, the relativistic and nonrelativistic bound state energies were obtained for some diatomic molecules such as (HCl, CH, LiH, CO, NO, O2, I2, N2, H2, and Ar2). The obtained energy eigenvalues appear as a function of the generalized Gamma function, the parameters of noncommutativity, and the parameters of studied potential, in addition to the atomic quantum numbers . In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present result is consistent with what is obtained in the literature. We have seen that the improved approximation of the centrifugal term is better than the other approximations in finding the approximate analytical solutions of the Klein-Gordon and Schrödinger equations for the modified Manning–Rosen potential in RNCQM and NRNCQM.
Using the supersymmetric quantum mechanics (SUSY) approach, we obtained analytical approximate solutions to the Dirac equation with an improved Tietz diatomic potential function under spin and pseudospin symmetries. The energy eigenvalues equation and the corresponding wave spinor for the two symmetries have been explicitly obtained. The non relativistic limit of the spin symmetry has been obtained. The solution of Morse, Deng-Fan, and Rosen-Morse were obtained by changing the numerical value of q We have also obtained the thermodynamic properties of a system under the improved Tietz potential function.