On bounds of \(N(\lambda)\) for a magnetic Schrödinger operator
The author considers the Schrödinger operator \(H\) in \(\mathbb{R}^2\) with magnetic potential. Let \(N(\lambda)\) denote the dimension of the spectral projection of \(H\) on \([0,\lambda]\) for \(\lambda>0\). A two-side estimate of \(N(\lambda)\) is proven and a similar estimate for the bottom of the spectrum is provided.
scientific article; zbMATH DE number 1425152
scientific article