On the Energy Levels of the Hydrogen Atom

Details On the Energy Levels of the Hydrogen Atom On the Energy Levels of the Hydrogen Atom

1993-05-21

arxiv.org/abs/hep-th/9305102v1

Physics

High Energy Physics

High Energy Physics - Theory

26pp, LaTeX. 1 figure available on request, DAMTP-R93/9

Scientific paper

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.

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