Two electrons in a homogeneous magnetic field: particular analytical solutions
- 7 February 1994
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 27 (3) , 1045-1055
- https://doi.org/10.1088/0305-4470/27/3/040
Abstract
Particular analytical solutions of the two-dimensional Schrodinger equation are described for two electrons (interacting with Coulomb potentials) in a homogeneous magnetic field B and an external oscillator potential with frequency omega 0. These exact solutions occur at an infinite and countable set of values of the quantity omega = square root ( omega 02+ 1/4 (B/c)2). Additionally, approximate closed-form solutions for the limits of small omega (perturbation theory in the electron-electron interaction) and large omega (harmonic approximation) are discussed and compared with the exact solutions.Keywords
This publication has 5 references indexed in Scilit:
- Spin-singlet–spin-triplet oscillations in quantum dotsPhysical Review B, 1992
- Energy spectra of two electrons in a harmonic quantum dotPhysical Review B, 1991
- Some magnetic properties of metals I. General introduction, and properties of large systems of electronsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1952
- The Diamagnetism of the Free ElectronMathematical Proceedings of the Cambridge Philosophical Society, 1931
- Bemerkung zur Quantelung des harmonischen Oszillators im MagnetfeldThe European Physical Journal A, 1928