Schroedinger upper bounds to semirelativistic eigenvalues
Richard L. Hall, Wolfgang Lucha
TL;DR
This paper develops a method to derive upper bounds for the eigenvalues of semirelativistic Hamiltonians using related Schrödinger operators, allowing for optimized parameter choices.
Contribution
It introduces a novel approach to bound semirelativistic eigenvalues via Schrödinger operators with tunable parameters, enhancing analytical tools in quantum mechanics.
Findings
Derived explicit upper bounds for semirelativistic eigenvalues.
Demonstrated the bounds include free parameters for optimization.
Provided a framework applicable to various potentials.
Abstract
Problems posed by semirelativistic Hamiltonians of the form H = sqrt{m^2+p^2} + V(r) are studied. It is shown that energy upper bounds can be constructed in terms of certain related Schroedinger operators; these bounds include free parameters which can be chosen optimally.
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