Accurate calculation of the complex eigenvalues of the Schr\"{o}dinger equation with an exponential potential

TL;DR

This paper demonstrates that the Riccati–Pade method effectively computes accurate complex eigenvalues for the Schrödinger equation with exponential potentials, showing high precision for realistic parameters.

Contribution

It introduces the Riccati–Pade method as a reliable technique for calculating complex eigenvalues in quantum systems with exponential potentials.

Findings

High accuracy in eigenvalue calculations for realistic parameters

Effective application of Riccati–Pade method to exponential potentials

Validation of the method's suitability for quantum eigenvalue problems

Abstract

We show that the Riccati--Pad\'{e} method is suitable for the calculation of the complex eigenvalues of the Schr\"{o}dinger equation with a repulsive exponential potential. The accuracy of the results is remarkable for realistic potential parameters.