Renormalization--Group Solutions for Yukawa Potential

TL;DR

This paper employs self-similar renormalization group methods to analytically determine the spectrum and critical screening parameter of the Yukawa potential, providing accurate results without extensive numerical computations.

Contribution

It introduces a renormalization-group approach to solve the Yukawa potential spectrum and critical screening, offering a more efficient alternative to numerical methods.

Findings

Accurate spectrum expressions for Yukawa potential

Critical screening parameter identified

Method reduces reliance on numerical calculations

Abstract

The self--similar renormalization group is used to obtain expressions for the spectrum of the Hamiltonian with the Yukawa potential. The critical screening parameter above which there are no bound states is also obtained by this method. The approach presented illustrates that one can achieve good accuracy without involving extensive numerical calculations, but invoking instead the renormalization--group techniques.