On Eigenfunction Decay for Two Dimensional¶Magnetic Schrödinger Operators

Abstract:

For two dimensional Schrödinger operators with a nonzero constant magnetic field perturbed by a magnetic field and a scalar potential, both vanishing arbitrarily slow at infinity, it is proved that eigenfunctions corresponding to the discrete spectrum decay faster than any exponential. Under more restrictive conditions on the perturbations, even quicker decay is obtained.