Quantized motion of three two-dimensional electrons in a strong magnetic field

We have found a simple, exact solution of the Schrödinger equation for three two-dimensional electrons in a strong magnetic field, given the assumption that they lie in a single Landau level. We find that the interelectronic spacing has characteristic values, not dependent on the form of the interaction, which change discontinuously as pressure is applied, and that the system has characteristic excitation energies of approximately $0.03\frac{e^2}{a_0}$, where $a_0$ is the magnetic length.