Klein-Gordon lower bound to the semirelativistic ground-state energy

TL;DR

This paper establishes a lower bound for the ground-state energy of a semirelativistic Hamiltonian using the Klein-Gordon problem, providing detailed results for specific potentials.

Contribution

It introduces a novel lower bound for semirelativistic energies based on Klein-Gordon solutions, applicable to attractive potentials that vanish at infinity.

Findings

Lower bound proven for semirelativistic ground-state energy.

Explicit results for exponential and Woods-Saxon potentials.

Method applicable to a class of attractive potentials.

Abstract

For the class of attractive potentials V(r) <= 0 which vanish at infinity, we prove that the ground-state energy E of the semirelativistic Hamiltonian H = \sqrt{m^2 + p^2} + V(r) is bounded below by the ground-state energy e of the corresponding Klein--Gordon problem (p^2 + m^2)\phi = (V(r) -e)^2\phi. Detailed results are presented for the exponential and Woods--Saxon potentials.