On eigenfunction decay for two dimensional magnetic Schrödinger operators (Q1268061)

The authors study the decay properties of the eigenfunctions for the magnetic Schrödinger operator \(H= (\vec p- \vec a(\vec x))^2+ V(\vec x)\), \(\vec x\in\mathbb{R}^2\). The main result is that if \(B'(\vec x)\), \(V(\vec x)\to 0\) as \(|\vec x|\to\infty\), then the eigenfunctions corresponding to \(E\not\in \sigma_L(B_0)\) (the Landau spectrum) decay faster than any exponential.