G. Coote

Sharp Computational Bounds for Spectral Types of Schr\"odinger Operators

We prove sharp bounds for determining the spectral-type decomposition of Schr\"odinger operators in the spirit of Smale's program on the foundations of computation. For explicit one-dimensional self-adjoint Schr\"odinger operators $H=-{\mathrm d^2}/{\mathrm dx^2}+V$ on $L^2(\mathbb R)$, where $V\in C^\infty(\mathbb R;\...