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A Note on the Quantum-Mechanical Perturbation Theory
Abstract
The solution of the quantum-mechanical eigenvalue problem is discussed for cases when a series of approximate eigenfunctions is known. If these ``unperturbed'' states are divided into two classes, a perturbation formula is derived giving the influence of one class of states on the other in the final solution. The formula contains as special cases: (i) the Schrödinger-Brillouin formula for the eigenvalue of a nondegenerate state, (ii) a new simple formula for treating a class of degenerate states, and (iii) the splitting of the secular equation in cases where the system naturally consists of two independent parts in mutual interaction.
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Cited by
Maximally localized Wannier functions: Theory and applications
Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I., & Vanderbilt, D. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1419 · Cited by 3,283
Pseudopotential methods in condensed matter applications
Pickett, W. E. (1989) · Computer Physics Reports · doi:10.1016/0167-7977(89)90002-6 · Cited by 915
Liu, G.-B., Xiao, D., Yao, Y., Xu, X., & Yao, W. (2015) · Chemical Society Reviews · doi:10.1039/c4cs00301b · Cited by 698
Stresses in semiconductors:Ab initio calculations on Si, Ge, and GaAs
Nielsen, O. H., & Martin, R. M. (1985) · Physical Review B · doi:10.1103/physrevb.32.3792 · Cited by 678
Theory of semiconductor superlattice electronic structure
Smith, D. L., & Mailhiot, C. (1990) · Reviews of Modern Physics · doi:10.1103/revmodphys.62.173 · Cited by 567
Metadata
- Authors
- Löwdin, P.-O.
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 1951-11-01
- Volume
- 19
- Issue
- 11
- Pages
- 1396-1401
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2116008596
- Cited by
- 944
- References
- 0
- FWCI
- 2.92
- Type
- journal article
- Language
- en
- Open access
- closed
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- Löwdin, P.-O. (1951). A Note on the Quantum-Mechanical Perturbation Theory. The Journal of Chemical Physics. https://doi.org/10.1063/1.1748067
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