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Chinese Journal of Physics

Analytical Solutions of the Klein-Gordon equation and Fisher information with Inversely Quadratic Hellman potential

Ifeanyi Jude Njoku, Chibueze Paul Onyenegecha, Chioma J. Okereke

Published Aug 19, 2022• 6 citations
Publisher
DOI
10.1016/j.cjph.2022.08.011

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Physica Scripta•Sep 19, 2023•3 citations
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.
Spatially quadratic deformation radial momentum of D-dimensional Klein-Gordon equation with three-dimensional Harmonic Oscillator and Inverse Quadratic potential was investigated using Hypergeometric Method. By using appropriate variable transformation, D-Dimensional Klein-Gordon equation for q deformed momentum was reduced into one order dimensional Schrodinger like equation with Pöschl-Teller like potential. The relativistic energy and wave function equations were obtained from the solution of Schrodinger like equation. Then, the relativistic energy and wave function were calculated and visualized using Matlab R2013 software, respectively. The q deformed parameter had the effect to the relativistic energy and wave function. The increase of q deformed parameter causes the increase of energy spectra and the decrease of amplitude.
Abstract We solved the Klein–Gordon equation for a generalized inverse quadratic Yukawa (GIQY) potential via path integrals approach. We applied approximations to deal with the terms 1/r 2 and 1/r. A path integral representation of Green’s function relating to a particle moving in a mixture of equal vector and scalar potentials was established. To integrate Green’s function, a space-time transformation was successfully used, and the present problem was reduced to a previously known modified Pöschl-Teller potential problem. The integrated Green’s function contains important information about the considered system, from which we obtained energy eigenvalues and the corresponding normalized eigenfunctions for various values of n and ℓquantum numbers. Numerical results, Schrödinger solutions, and special cases such as the modified screened Coulomb plus inversely quadratic Yukawa potential, Kratzer potential, Yukawa potential, and Coulomb potential were also considered. These results are largely consistent with previous studies.