SCATTERING PROBLEM FOR THE VALENCE ELECTRON MODEL POTENTIAL

Authors

  • Anzor Khelashvili Inst. of High Energy Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia
  • Teimuraz Nadareishvili Department of Physics, Faculty of Exact and Natural Sciences, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia

DOI:

https://doi.org/10.61841/v9p24m33

Keywords:

Self-adjoint extension, Schrodinger equation, additional solutions, scattering amplitude, valence electron model

Abstract

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,” Physical Review A, 109, 062205 (2024).

B. Blaschke, P. Beneš, “All finite-mass Dirac monopoles,” Physical Review 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,” Physical Review Letters, 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,” Journal of Physics A: Mathematical and General, 28, 2359 (1995).

A. Khelashvili, 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, T. Nadareishvili, “Self-conjunction extension procedure for a singular oscillator,” Georgian Electronic Scientific Journal (GESJ), No.1(30) (2024), pp. 33–44.

A. Khelashvili, T. Nadareishvili, “Pragmatic Self-adjoint procedure in the Schrödinger equation for the inverse square potential,” Georgian Electronic Scientific Journal (GESJ), No.2(29) (2023), pp. 36–49.

A. Khelashvili, T. Nadareishvili, “Pragmatic Self-adjoint extension (SAE) procedure in the Schrödinger equation for the bound and scattering states of the inverse square attractive potential in 3 dimensions,” Submitted to Physics of Particles and Nuclei Letters.

W. Krolikowski, Bulletin de l’Académie Polonaise, Vol. 18, 83 (1979).

M. I. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards: Applied Mathematics Series–55 (1964).

L. Landau, E. D. Lifshitz, Quantum Mechanics, Oxford: Pergamon (1977).

H. Pilkuhn, Relativistic Particle Physics, Springer (1979).

Downloads

Published

2025-04-20

How to Cite

Khelashvili, A., & Nadareishvili, T. . (2025). SCATTERING PROBLEM FOR THE VALENCE ELECTRON MODEL POTENTIAL. Journal of Advance Research in Applied Science (ISSN 2208-2352), 11(1), 44-51. https://doi.org/10.61841/v9p24m33