1996/09/11 by Wolfgang Lucha, Franz F. Schöberl · 1 citation
Mathematics · Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #hep-ph #hep-th
paper · pdf · doi:10.1103/physreva.56.139
published as Phys.Rev.A56:139-145,1997 · 16 pages, LaTeX
arxiv created 1996/09/11 · openalex publication_date 1997/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The spinless Salpeter equation may be considered either as a standard approximation to the Bethe-Salpeter formalism, designed for the description of bound states within a relativistic quantum field theory, or as the most simple, to a certain extent relativistic, generalization of the costumary nonrelativistic Schr"odinger formalism. Because of the presence of the rather difficult-to-handle square-root operator of the relativistic kinetic energy in the corresponding Hamiltonian, very frequently the corresponding (discrete) spectrum of energy eigenvalues cannot be determined analytically. Therefore, we show how to calculate, by some clever choices of basis vectors in the Hilbert space of solutions, for the rather large class of power-law potentials, at least upper bounds on these energy eigenvalues. For the lowest-lying levels, this may be done even analytically.