Solution Analysis for D-Dimensional Cosmic String Coupled by Hyperbolic Scarf Plus Poschl-Teller and Manning-Rosen Potentials

A. Suparmi, Dian Anggraini, C. Cari, Suci Faniandari

Abstract

Wave function and energy spectra for a d-dimension time-independent cosmic string with the radial hyperbolic scarf and angular Poschl-Teller non-central potential had been investigated with the hypergeometric method. The aim of this work was to obtain the solution and analyze the energy level, wave function, and its application in the Renyi entropy and the Schwarzschild black hole. The equation for d-dimension time-independent cosmic string was reduced into a d-dimension Schrodinger-like equation. The variable separation method was applied to resolve the equation into d’s one-dimensional Schrodinger-like equations. Each of d’s one-dimensional Schrodinger-like equations was analyzed by using the hypergeometric method to obtain wave function and energy equations. The energy equation was obtained from the solution of the radial part. Wave functions were obtained from the solution of the radial and angular parts. The energy levels were higher in the presence of Hyperbolic Scarf plus Poschl-Teller and Manning-Rosen potentials. Numerical results of energy levels showed that the energy level increased a similar amount to the increase of potential parameters. The form of the plot of energy levels as a function of the cosmic string parameter showed the quartic function. This solution was applied to determine the thermodynamic properties of the Schwarzschild black hole which has not been reported in previous works. This information can be used for future research of the properties of the Schwarzschild black hole.

 

Keywords: wave function, energy spectra, cosmic string, hyperbolic scarf potential.


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