Abstract
Unfortunately, it is impossible to obtain analytic solutions of the Schrödinger equation for most potentials. However there is a large class of problems in quantum mechanics where the Hamiltonian consists of two parts. The first part corresponds to an isolated quantum system, such as a hydrogen atom, for which we know the exact eigenfunctions and eigenenergies. The second part of the Hamiltonian corresponds to the interaction of the isolated quantum system with some external potential. If the second potential is weak (and I have to define what I mean by weak), it is possible to develop a systematic procedure to approximate the eigenfunctions and eigenvalues of the total Hamiltonian. This procedure is referred to as perturbation theory.
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
Linus Pauling and J. Y. Beach, The van der Waals Interaction of Hydrogen Atoms, Physical Review 47, 686–692 (1935).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Berman, P.R. (2018). Perturbation Theory. In: Introductory Quantum Mechanics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-68598-4_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-68598-4_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-68596-0
Online ISBN: 978-3-319-68598-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)