Self-adjoint extensions for confined electrons: From a particle in a spherical cavity to the hydrogen atom in a sphere and on a cone

Al-Hashimi, Munir; Wiese, Uwe-Jens (2012). Self-adjoint extensions for confined electrons: From a particle in a spherical cavity to the hydrogen atom in a sphere and on a cone. Annals of physics, 327(11), pp. 2742-2759. Kidlington, UK: Elsevier 10.1016/j.aop.2012.06.006

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In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states localized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge–Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r1/r potential.

Item Type:	Journal Article (Original Article)
Division/Institute:	08 Faculty of Science > Institute of Theoretical Physics
UniBE Contributor:	Al-Hashimi, Munir, Wiese, Uwe-Jens
Subjects:	500 Science > 530 Physics
ISSN:	0003-4916
Publisher:	Elsevier
Language:	English
Submitter:	Esther Fiechter
Date Deposited:	04 Oct 2013 14:41
Last Modified:	05 Dec 2022 14:13
Publisher DOI:	10.1016/j.aop.2012.06.006
Web of Science ID:	000308687500006
ArXiv ID:	1204.3434
URI:	https://boris.unibe.ch/id/eprint/16996 (FactScience: 224712)