Analytical Treatment of the Oscillating Yukawa Potential

TL;DR

This paper presents an analytical approach to solving the oscillating Yukawa potential using a Laguerre basis set, enabling the calculation of bound states and resonances with high accuracy.

Contribution

It introduces a novel analytical method employing a Laguerre basis for the Yukawa potential with complex screening, allowing simultaneous treatment of cosine and sine-like potentials.

Findings

Closed-form matrix elements for the Yukawa potential were derived.

Bound state spectra were computed analytically as eigenvalues.

Resonance energies were accurately evaluated using a complex scaling method.

Abstract

Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate in closed form the matrix elements of the generalized Yukawa potential with complex screening parameter. This enabled us to treat analytically both the cosine and sine-like Yukawa potentials on equal footing and compute their bound states spectrum as the eigenvalues of the associated analytical matrix representing their Hamiltonians. Finally we used a carefully designed complex scaling method to evaluate the resonance energies and compared our results satisfactorily with those obtained in the literature.