Spectral bounds for the Hellmann potential

TL;DR

This paper develops simple formulas to bound the energy levels of a quantum system with the Hellmann potential, aiding in understanding its bound states without solving the Schrödinger equation exactly.

Contribution

It introduces new spectral bounds for the Hellmann potential using the potential envelope method, providing a practical tool for spectral analysis.

Findings

Derived upper and lower bounds for all energy eigenvalues.

Applicable to both positive and negative B in the potential.

Simplifies spectral analysis of the Hellmann potential.

Abstract

The method of potential envelopes is used to analyse the bound state spectrum of the Schroedinger Hamiltonian H=-\Delta+V(r), where the Hellmann potential is given by V(r) = -A/r + Be^{-Cr}/r, A and C are positive, and B can be positive or negative. We established simple formulas yielding upper and lower bounds for all the energy eigenvalues.