Rayleigh-Schrodinger perturbation theory with a strong perturbation: anharmonic oscillators
- 1 April 1986
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 19 (5) , 683-690
- https://doi.org/10.1088/0305-4470/19/5/021
Abstract
The bound state solutions of Schrodinger's equation for the anharmonic oscillator potentials V=x2+ lambda x2k (k=2,3, . . . ) have been investigated, using elementary techniques of low-order variational perturbation theory. For the quartic oscillator (k=2) a scaled harmonic potential provides a remarkably accurate model for all lambda . Although this model is slightly less satisfactory for higher-order anharmonicities (k>or=3), the perturbation procedures remain effective, and can be applied successfully provided that higher-order terms are calculated.Keywords
This publication has 15 references indexed in Scilit:
- The operator method of the approximate description of the quantum and classical systemsJournal of Physics A: General Physics, 1984
- Stark effect of a rigid rotorJournal of Physics B: Atomic and Molecular Physics, 1984
- Rayleigh-Schrodinger perturbation theory with a strong perturbation: the quadratic Zeeman effect in hydrogenJournal of Physics B: Atomic and Molecular Physics, 1984
- The operator method of the approximate solution of the Schrödinger equationPhysics Letters A, 1982
- Large order perturbation theory in the context of atomic and molecular physics—interdisciplinary aspectsInternational Journal of Quantum Chemistry, 1982
- Renormalised perturbation seriesJournal of Physics A: General Physics, 1981
- Quantum-mechanical perturbation theoryReports on Progress in Physics, 1977
- Eigenvalues of λx2m anharmonic oscillatorsJournal of Mathematical Physics, 1973
- Anharmonic OscillatorPhysical Review B, 1969
- A Perturbation-Variation Calculation of EigenvaluesProceedings of the Physical Society, 1961