Related papers: One-dimensional hydrogenic ions with screened nuclear Coulomb field

One-dimensional hydrogenic ions with screened nuclear Coulomb field

URL: http://arxiv.org/abs/2312.04033v2
Date: Tue, 30 Jul 2024 20:57:04 GMT
Title: One-dimensional hydrogenic ions with screened nuclear Coulomb field
Authors: Suchindram Dasgupta, Chirag Khurana, A. Shadi Tahvildar-Zadeh,
Abstract summary: We study the spectrum of the Dirac hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus. We show that the essential spectrum has the usual gap $(-mc2,mc2)$ in it, and that there are only finitely many eigenvalues in that gap.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We study the spectrum of the Dirac hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the nucleus is assumed fixed at the origin. The potential is screened at large distances so that it goes to zero exponentially at spatial infinity. We show that the hamiltonian is essentially self-adjoint, the essential spectrum has the usual gap $(-mc^2,mc^2)$ in it, and that there are only finitely many eigenvalues in that gap, corresponding to ground and excited states for the system. We find a one-to-one correspondence between the eigenfunctions of this hamiltonian and the heteroclinic saddle-saddle connectors of a certain dynamical system on a finite cylinder. We use this correspondence to study how the number of bound states changes with the nuclear charge.

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