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.
Keywords
EigenfunctionDegenerate energy levelsEigenvalues and eigenvectorsMathematicsQuantumPerturbation (astronomy)Mathematical physicsPerturbation theory (quantum mechanics)Quantum mechanicsSchrödinger equationPure mathematicsMathematical analysisPhysics
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Publication Info
- Year
- 1951
- Type
- article
- Volume
- 19
- Issue
- 11
- Pages
- 1396-1401
- Citations
- 938
- Access
- Closed
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Cite This
Per‐Olov Löwdin
(1951).
A Note on the Quantum-Mechanical Perturbation Theory.
The Journal of Chemical Physics
, 19
(11)
, 1396-1401.
https://doi.org/10.1063/1.1748067
Identifiers
- DOI
- 10.1063/1.1748067