Scattering states solutions of Klein–Gordon equation with three physically solvable potential models

Abstract

The scattering state solutions of the Klein-Gordon equation with equal scalar and vector Varshni, Hellmann and Varshni-Shukla potentials for any arbitrary angular momentum quantum number are investigated within the framework of the functional analytical method using a suitable approximation. The asymptotic wave functions, approximate scattering phase shifts, normalization constants and bound state energy equations were obtained. The nonrelativistic limits of the scattering phase shifts and the bound states energy equations for the three potentials were also obtained. Our bound states energy equations are in excellent agreement with the available ones in the literature. Our numerical and graphical results indicate the dependence of phase shifts on the screening parameter , the potential parameter and angular momentum quantum number .

Topological effects produced by point-like global monopole with Hulthen plus screened Kratzer potential on Eigenvalue solutions and NU-method

“…Equation (38) is the energy levels and equation (39) is the radial wave function of a non-relativistic particle confined by the Aharonov-Bohm flux field with Varshni potential in point-like defect. One can see the that the presence of topological defects of point-like defect characterise by the parameter α and the magnetic flux Φ influences the energy levels and the wave functions and modified them in comparison to those results obtained in [65][66][67][68][69] in the flat space background. In [70], authors studied the non-relativistic quantum system in 2D under an external magnetic and AB-flux fields in a cosmic string space-time with this Varshni potential.…”

“…where a and b are the strengths of the Varshni potential, respectively and δ is the screening parameter which controls the shape of the potential energy curve. This potential is a repulsive short-range potential that plays an important role in chemical, particle and molecular physics and many authors have been studied wave equations with this potential [65][66][67][68][69][70].…”

Approximate Scattering State Solutions of DKPE and SSE with Hellmann Potential

“…(2) The effect of total angular momentum centrifugal term in Eq. ( 2) can be subdued using approximation scheme of the type [7,10,14] 1…”

Thermal Properties and Magnetic Susceptibility of Hellmann Potential in Aharonov–Bohm (AB) Flux and Magnetic Fields at Zero and Finite Temperatures

“…Subsequently, several investigations was carried out with this potential; for instance, it has been applied to study bound state problems using different advanced mathematical techniques [5,6]. The Hellmann potential have been put to use to study the approximate scattering state solutions in the relativistic regime [7][8][9]. The applications of this potential model include the following amongst many others; atomic physics and neutron scattering electron-core [10,11], "electron-ion" [12], "inner-shell ionization problem", "alkali hydride molecules" and in condensed matter physics [13,14].…”

“…shows that the partition function decreases as  increases. In Fig (9),. the relationship between magnetization, shows a pseudo-sinusoid in the region 13 B .…”