1993/05/21 by Christopher J. Fewster, C. J. Fewster, Fewster, C. J. · 1 citation
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Quantum chaos and dynamical systems #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9305102
26pp, LaTeX. 1 figure available on request, DAMTP-R93/9
arxiv created 1993/05/21 · openalex publication_date 1993/05/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We re-examine the justification for the imposition of regular boundary conditions on the wavefunction at the Coulomb singularity in the treatment of the hydrogen atom in non-relativistic quantum mechanics. We show that the issue of the correct boundary conditions is not independent of the physical structure of the proton. Under the physically reasonable assumption that the finite size and structure of the proton can be represented as a positive correction to the Coulomb potential, we give a justification for the regular boundary condition, which, in contrast to the usual treatments, is physically motivated and mathematically rigorous. We also describe how irregular boundary conditions can be used to model non-positive corrections to the Coulomb potential.