TITLE:
On the Use of Perturbation Theory in Eigenvalue Problems
AUTHORS:
Arij A. Awin, Bashir W. Sharif, Ali M. Awin
KEYWORDS:
Perturbation, Eigenvalue, Hamiltonian, Quantum, Mechanics
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.9,
September
15,
2021
ABSTRACT: The importance of perturbation theory in many fields is very clear through almost a century or even more. Its importance was exemplified in solving many problems in physics and other applied fields. A great deal of applications arose in dealing with eigenvalue problems especially in quantum mechanics in conjunction with the field of atomic physics. Accordingly, it came to our mind to write a brief review article on the subject. At the beginning, we give some important definitions to do with various eigenvalue problems; then we introduce concepts that have to do with perturbation theory and the techniques used in such a theory, beginning with the algebraic perturbation theory giving a good number of examples from the literature on the use of the theory in solving integral equation, algebraic equations and differential equations. Few applications are then given in applied fields such as classical mechanics, quantum mechanics and fluid mechanics. Finally, a concluding discussion is given which is related to the use of the theory.