Matrix elements in harmonic oscillator representations I. General solution and application to one dimension
- 1 June 1970
- journal article
- Published by IOP Publishing in Journal of Physics B: Atomic and Molecular Physics
- Vol. 3 (6) , 735-744
- https://doi.org/10.1088/0022-3700/3/6/001
Abstract
General expressions have been obtained for the matrix elements of linear or radial perturbations in the representations of the one-, two-, and three-dimensional harmonic oscillators. The solutions are also general for the two types of matrix element where the two wave functions belong to the same basis set or to two different basis sets. In this paper these expressions are applied to one- dimensional problems.Keywords
This publication has 17 references indexed in Scilit:
- Gaussian perturbations to harmonic oscillatorsJournal of Physics B: Atomic and Molecular Physics, 1969
- Lingering Time of the Proton in the Wells of the Double-Minimum Potential of Hydrogen BondsThe Journal of Chemical Physics, 1969
- Tridiagonalization of a symetric band matrixNumerische Mathematik, 1968
- Energy Corrections for the Potential a(x4 − bx2)The Journal of Chemical Physics, 1968
- TheQR andQL algorithms for symmetric matricesNumerische Mathematik, 1968
- Overlap integral of three-dimensional isotropic harmonic oscillator wave functionsJournal of Molecular Spectroscopy, 1967
- Vibronic intensity distributions in the electronic spectra of polyatomic moleculesProceedings of the Physical Society, 1966
- Overlap integral of two-dimensional isotropic harmonic oscillator wavefunctionsJournal of Molecular Spectroscopy, 1966
- Some energy levels and matrix elements of the quartic oscillatorJournal of Molecular Spectroscopy, 1963
- The occurrence and properties of molecular vibrations withV(x) =ax4Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1945