Exponential decay of eigenfunctions of Schrödinger operators with magnetic fields
The author analyzes the essential spectrum and the decay of the eigenfunctions for the Schrödinger operator on \(L^2(\mathbb{R}^\nu)\) \[ {\mathcal H}= \sum_{1\leq j,k \leq \nu} (D_j-A_j) g_{jk} (D_k-A_k) +V, \] with an electric potential \(V\), a magnetic potential \(\vec A\) and a metric \(g_{jk}\) which may be unbounded at \(\infty\). The author proposes various extensions of results by \textit{S. Agmon} [Lectures on exponential decay of solutions of second-order elliptic equations. Math. Notes Princeton Univ. Press 29 (1982; Zbl 0503.35001)] by permitting for example singularities for the magnetic potential. He also analyzes the case of \(N\)-body Hamiltonians.
scientific article; zbMATH DE number 1006819