Hydrogen atom in the four-dimensional oscillator representation: matrix elements of zn
- 1 October 1985
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 18 (14) , 2719-2727
- https://doi.org/10.1088/0305-4470/18/14/022
Abstract
The authors presents a calculation of the matrix elements of zn between four-dimensional harmonic oscillator states. It is shown that a knowledge of the scalar product of two harmonic oscillator states of different frequencies is enough to generate the matrix elements of any power of z. These can be found by taking appropriate derivatives of the aforementioned scalar product.Keywords
This publication has 17 references indexed in Scilit:
- Stochastic ionization of surface-state electrons: Classical theoryPhysical Review A, 1984
- Quantum Mechanical Suppression of Classical Stochasticity in the Dynamics of Periodically Perturbed Surface-State ElectronsPhysical Review Letters, 1984
- Quantum dynamics and nonintegrabilityPhysical Review A, 1983
- Stochastic Ionization of Surface-State ElectronsPhysical Review Letters, 1982
- Theory of nonbijective canonical transformations in mechanics: Application to the Coulomb problemJournal of Mathematical Physics, 1982
- Homeomorphism connecting the hydrogenic system and the free-particle systemPhysical Review A, 1982
- Hydrogen atom as a four-dimensional oscillatorPhysical Review A, 1980
- Quantum theory of infinite component fieldsJournal of Mathematical Physics, 1979
- Observation of Resonances in the Microwave-Stimulated Multiphoton Excitation and Ionization of Highly Excited Hydrogen AtomsPhysical Review Letters, 1977
- The three-dimensional hydrogen atom as a restricted four-dimensional harmonic oscillatorPhysica, 1973