APPLIED JOURNAL OF PHYSICAL SCIENCE
Integrity Research Journals
ISSN: 2756-6684
Model: Open Access/Peer Reviewed
DOI: 10.31248/AJPS
Start Year: 2018
Email: ajps@integrityresjournals.org
Non-degenerate fourth order perturbation theory
https://doi.org/10.31248/AJPS2019.020 | Article Number: 538B15B51 | Vol.2 (2) - June 2020
Received Date: 07 October 2019 | Accepted Date: 19 November 2019 | Published Date: 30 June 2020
Authors: Gilbert A. Ibitola* , Olanrewaju Ajanaku and Abiola O. Ilori
Keywords: Energy states, first-order, fourth-order, Hamiltonian, perturbation, perturbation-free, perturbed, second–order, third-order, unperturbed state, wave function.
There exist several forms of perturbation theory in Quantum Mechanics, namely: non-degenerate perturbation theory, degenerate perturbation theory, time-dependent perturbation theory, time-constant perturbation theory and time-harmonic perturbation theory. This paper presents an extension of the perturbation theory for non-degenerate states. It has been observed that most texts and journal papers treat only the first –order and second-order non-degenerate perturbation theory. Therefore, this paper attempts to treat and present the third order and fourth order non-degenerate perturbation theory in quantum mechanics. It can thus be asserted that the higher the order of perturbations of quantum systems that we know, the more successful will be our efforts in suppressing or eliminating them.
| Abrikosov, A. A., Gorkov, L. P., & Dzyaloshinski, I. E. (1995). Quantum field theory. Dover (NY) Publishers. Pp. 67-75. | ||||
| Avron, J. E., Seiler, R., & Simon, B. (1994). Charge deficiency, charge transport and comparison of dimensions. Communications in mathematical physics, 159(2), 399-422. Crossref |
||||
| Bell, W. W. (2004). Special functions for scientists and engineers", Dover Publication Inc., New York, United States. Pp.126-152. | ||||
| Condon, E. U., & Shortley, G. H. (1990). The theory of atomic spectra. Cambridge University Press, Cambridge. Pp. 56-61. | ||||
| Fermi, E. (1971). Notes on quantum mechanics. The University of Chicago Press, Chicago. Pp. 107-113. | ||||
| Flugge, S. (1994). Quantum mechanics. Springer-Verlag, New York. Pp. 123-127. | ||||
| Goldman, I. I., & Krivchenkov, V. D. (2003). Problems in quantum mechanics. Dover Publications, New York. Pp. 75-87. | ||||
| Mandl, F. (1987). Quantum mechanics. Butterworks, London. Pp. 101-111. | ||||
| Marston, J. B., & Affleck, I. (1998). Field theory analysis of a short-range pairing model. Journal of Physics C: Solid State Physics, 21(13), 2511. Crossref |
||||
| Nomura T., & Yamada K. (2003). Higher order perturbation expansion for pairing interaction in repulsive Hubbard Model. Journal of the Physical Society of Japan, 72(8), 2053-2063. Crossref |
||||
| Sasaki, S., Ikeda, H., & Yamada, K., (2005). Fourth order perturbation theory for normal self-energy in repulsive Hubbard Model. Journal of the Physical Society of Japan, 74(9), 2592-2597. Crossref |
||||
Copyright © 2024 Integrity Research Journals. All rights reserved.