Renormalised perturbation theory for a general D-dimensional isotropic anharmonic oscillator
- 11 May 1984
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 17 (7) , 1449-1460
- https://doi.org/10.1088/0305-4470/17/7/012
Abstract
Hypervirial theorems are applied in order to obtain easily perturbation series (PS) for eigenenergies and expected values of power of the radial coordinate of a general D-dimensional isotropic anharmonic oscillator (IAO(D)). In the next step the renormalisation method is introduced to obtain renormalised PS allowing the eigenenergies of IAO(D) to be calculated with a high accuracy in a whole range of quantum numbers n, l and for high anharmonic constants.Keywords
This publication has 19 references indexed in Scilit:
- Eigenvalues of an anharmonic oscillatorJournal of Mathematical Physics, 1981
- Perturbation theory and hypervirial theorems for the anharmonic oscillatorPhysics Letters A, 1980
- Rearranged Perturbation Theory for the Schrödinger EquationPhysica Scripta, 1980
- Energy approximants and perturbation theoryPhysics Letters A, 1979
- Accurate energy levels for the anharmonic oscillator and a summable series for the double-well potential in perturbation theoryAnnals of Physics, 1979
- Hypervirial theorems applied to the perturbation theory for screened Coulomb potentialsPhysical Review A, 1979
- Quantum theory of anharmonic oscillators. I. Energy levels of oscillators with positive quartic anharmonicityJournal of Mathematical Physics, 1975
- The three-dimensional quartic oscillatorJournal of Physics B: Atomic and Molecular Physics, 1970
- The one- and two-dimensional quartic oscillatorsJournal of Physics B: Atomic and Molecular Physics, 1970
- Classical and Quantum Mechanical Hypervirial TheoremsThe Journal of Chemical Physics, 1960