Studies on the bound-state spectrum of hyperbolic potential

TL;DR

This paper employs a generalized pseudospectral method to accurately compute the bound-state spectrum of hyperbolic potentials, achieving high precision for various quantum states and exploring parameter effects in detail.

Contribution

It introduces an efficient numerical approach for solving the Schrödinger equation for hyperbolic potentials, providing highly accurate eigenvalues and eigenfunctions, including new states and detailed parameter analysis.

Findings

Eigenvalues accurate up to tenth decimal place.

Excellent agreement with existing literature.

Identification of new bound states.

Abstract

Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant non-relativistic Schr\"odinger equation allowing a non-uniform, optimal spatial discretization. Eigenvalues accurate up to tenth decimal place are reported for a large range of potential parameters; thus covering a wide range of interaction. Excellent agreement with available literature results is observed in all occasions. Special attention is paid for higher states. Some new states are given. Energy variations with respect to parameters in the potential are studied in considerable detail for the first time.