Interacting electrons in magnetic fields: Tracking potentials and Jastrow-product wavefunctions

摘要

The Schrodinger equation for an interacting spinless electron gas in anonuniform magnetic field admits an exact solution in Jastrow product form whenthe fluctuations in the magnetic field track the fluctuations in the scalarpotential. For tracking realizations in a two-dimensional electron gas, thedegeneracy of the lowest Landau level persists, and the ``tracking'' solutionsspan the ground state subspace. In the context of the fractional quantum Hallproblem, the Laughlin wave function is shown to be a tracking solution.Tracking solutions for screened Coulomb interactions are also constructed. Theresulting wavefunctions are proposed as variational wave functions withpotentially lower energy in the case of non-negligible Landau level mixing thanthe Laughlin function.