Schroedinger secant lower bounds to semirelativistic eigenvalues

TL;DR

This paper establishes lower bounds for the ground-state eigenvalues of semirelativistic Hamiltonians using Schroedinger operator bounds, providing a new analytical tool for spectral analysis in relativistic quantum mechanics.

Contribution

It introduces a method to bound semirelativistic eigenvalues from below by relating them to non-relativistic Schroedinger operators, a novel approach in spectral theory.

Findings

Ground-state eigenvalues are bounded below by Schroedinger operators with adjusted parameters.

The method applies to Hamiltonians of the form sqrt(m^2 + p^2) + V.

An example illustrates the effectiveness of the bounds.

Abstract

It is shown that the ground-state eigenvalue of a semirelativistic Hamiltonian of the form H = sqrt(m^2+p^2) + V is bounded below by the Schroedinger operator m + beta p^2 + V, for suitable beta > 0. An example is discussed.