Improved variational approach for the Cornell potential

TL;DR

This paper develops an improved variational method to approximate radial wave functions for the Cornell potential, effectively modeling quark-antiquark interactions with results closely matching numerical solutions.

Contribution

It introduces a variational approach that optimally determines parameters using the virial theorem and minimal discrepancy, enhancing accuracy for the Cornell potential.

Findings

Good agreement with exact numerical results

Effective variational parameters determination

Improved approximation of radial wave functions

Abstract

The approximate radial wave functions for the Cornell potential describing quark-antiquark interaction are constructed in the framework of a variational method. The optimal values of the variational parameters are fixed by the fulfillment of the requirements of the virial theorem and the minimality condition for integral discrepancy. The results of calculation with the simple trial function are in a good agreement with exact numerical results.