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Communications in Theoretical Physics

Relativistic Treatment of Spinless Particles Subject to a Tietz—Wei Oscillator

Guo-Hua Sun, Shi-Hai Dong

Published Aug 1, 2012• 38 citations
Publisher

Abstract

The bound state solutions of the relativistic Klein—Gordon equation with the Tietz—Wei diatomic molecular potential are presented for the s wave. It is shown that the solutions can be expressed by the generalized hyper geometric functions. The normalized wavefunctions are also derived.
DOI
10.1088/0253-6102/58/2/04

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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.
The scattering and bound states of relativistic spinless particles with position-dependent mass are investigated in the framework of the improved Frost-Musulin potential, which is used to explain some properties of diatomic molecules. After we obtain approximate analytical solution of the Klein-Gordon equation, we find the normalized wave functions in terms of the hypergeometric functions in order to deal with the bound and the scattering states. We also analyze the scattering phase shifts and the bound states numerically.
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.