Spectral bounds for the cutoff Coulomb potential

TL;DR

This paper introduces spectral bounds for the bound states of the Schrödinger Hamiltonian with a cutoff Coulomb potential, providing simple formulas for energy limits.

Contribution

It develops a potential envelope method to derive universal upper and lower bounds for all eigenvalues of the cutoff Coulomb potential.

Findings

Derived explicit formulas for energy bounds.

Validated bounds for all eigenvalues.

Applicable to potentials with cutoff parameters.

Abstract

The method of potential envelopes is used to analyse the bound-state spectrum of the Schroedinger Hamiltonian H = -Delta -v/(r+b), where v and b are positive. We established simple formulas yielding upper and lower energy bounds for all the energy eigenvalues.