Analysics of energy and wave function in the presence of a minimal length formalism for Yukawa potential using hypergeometry method and Q deformed potential

Abstract

The application of minimal length formalism in Schrodinger equation with Yukawa potential was studied in the case of scalar potential that was equal with vector potential. By using the approximate new wave function and simple mathematical manipulation, the Schrodinger equation with Yukawa potential within minimal length formalism reduced to the Schrodinger equation with q deformed hyperbolic central potential. The non relativistic energy equation and wave function of Schrodinger equation with q deformed hyperbolic central potential was obtained by using the Asymptotic Iteration Method. By using the Matlab software, energy spectra were calculated numerically from non relativistic energy equation. The un-normalized wave function was expressed in hypergeometric terms. The presence of the minimal length parameter caused the change of the energy spectra. For the larger values of potential depth (Vo) at the value of the minimal length parameter, αML = 0.1 and at with zero orbital quantum number, caused the energy spectra decreasing both for system with minimal length or without minimal length. The width of potential (ξ) caused the energy spectra with minimal length parameter of the system increasing but the energy spectra without minimal length parameter of the system decreasing. However, for the smaller value of the minimal length parameter and at any values of the orbital quantum number the energy spectra fastly decreased compared to the energy spectra without the presence of minimal length.