2 ELECTRONS IN A HOMOGENEOUS MAGNETIC-FIELD - PARTICULAR ANALYTICAL SOLUTIONS

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 omega0. These exact solutions occur at an infinite and countable set of values of the quantity omega = square-root omega0(2) + 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.