1999/05/31 by Wolfgang Lucha, Franz F. Schöberl, F. F. Schoberl · 10 citations
Mathematics · Physics and Astronomy · #Computer science #Constant (computer programming) #Coulomb #Coupling (piping) #Coupling constant #Dimension (graph theory) #Eigenvalues and eigenvectors #Electron #Mathematical analysis #Mathematics #Nuclear physics research studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Spectral Theory in Mathematical Physics #Upper and lower bounds #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/1.533211
published in Journal of Mathematical Physics 41(4), 1778-1787 (American Institute of Physics) · LaTeX, 11 pages
arxiv created 1999/05/31 · openalex publication_date 2000/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Motivated by a recent analysis that presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a (“hard-core amended”) Coulomb interaction potential in one dimension. We prove the existence of a critical coupling constant (which contradicts the assertions of the previous analysis) and give analytic upper bounds on the energy eigenvalues. These upper bounds seem to disprove the previous explicit solution.