Scattering problem for the valence electron model potential
DOI:
https://doi.org/10.61841/v9p24m33Abstract
In the paper, in the scattering problem for the valence electron model potential a self-adjoint extension is performed and Rutherford formula is modified. The scattering of slow particles for this potential is also discussed and the changes caused by the self-adjoint extension in the differential and integral cross-sections of the scattering are studied.
References
J.V.S. Scursulim, A. A. Lima, U.Camera da Silva, G. Sotkov, ’’Supersymmetry shielding the scaling symmetry of conformal quantum mechanics’’, Physical Review A, 101, 032105 (2020)
Pablo L. Saldanha, ’’Gauge invariance of the Aharonov-Bohm effect in a quantum electrodynamics framework’’. Phys. Rev. A 109, 062205 (2024).
B. Blaschke, P. Beneš, ’’All finite-mass Dirac monopoles’’, Phys.Rev.D 106,125014 (2022).
I.Fernández,N.Holzmann,G. Frenking, "The Valence Orbitals of the Alkaline-Earth Atoms". Chemistry: A European Journal, 26 (62),14194(2020).
Yong Xiao, Yu Tian, Yu-Xiao Liu, ’’Extended black hole thermodynamics from extended Iyer-Wald formalism’’. Phys. Rev. Lett. 132, 021401(2024)
R.Yadav, A. Khare, N.Kumari , B. Mandal, ’’Rationally extended many-body truncated Calogero–Sutherland model’’. Annals of Physics, 400, 189 (2019).
J.Audretsch , U.Jasper, V.D. Skarzhinsky, ’’A pragmatic approach to the problem of the self-adjoint extension of Hamilton operators with the Aharonov-Bohm potential’’, J.Phys.A:Math.Gen, 28, 2359 (1995).
A. Khelashvili and T. Nadareishvili. ’’Singular behavior of the Laplace operator in polar spherical coordinates and some of its consequences for the radial wave function at the origin of coordinates’’. Physics of Particles and Nuclei Letters.,12,11.(2015)
A. Khelashvili and T. Nadareishvili. ’’Self -conjuction extension procedure for a singular oscillator’’. Geogian Electronic Scientific Journal (GESJ).No.1(30) [2024.06.30](2024).pp. 33-44
A. Khelashvili and T. Nadareishvili.’’Pragmatic Self-adjoint procedure in the Schrodinger equation fo the inverse square potential’’. Geogian Electronic Scientific Journal (GESJ).No.2(29) [2023.12.31](2023).pp. 36-49
A. Khelashvili and T. Nadareishvili. ’’Pragmatic Self-adjoint extension (SAE) procedure in the Schodinger equation for the bound and scattering states of the inverse square attractive potential in 3 dimensions’’. Submitted to the Physics of Particles and Nuclei Letters.
W.Krolikowski;Bulletin De Lacademics polonaise.Vol 18,83 (1979).
M.I. Abramowitz I.A. Stegun. 1964 Handbook of Mathematical functions (USA: National Bureau of Standards. Applied Mathematics Series – 55)(1964).
L. Landau and E. D Lifshitz. Quantum Mechanics (Oxford: Pergamon) (1977).
H. Pilkuhn.Relativistic Particle Physics (Springer) (1979)
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Teimuraz Nadareishvili, Annzor Khelasvili

This work is licensed under a Creative Commons Attribution 4.0 International License.
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.