Quantitative Local Weyl Laws for Schrodinger Operators with Non-Smooth Potentials
Weyl's law counts the eigenvalues of a semiclassical Schrodinger operator by a phase-space volume as Planck's constant tends to zero; the quantitative version supplies an explicit convergence rate. Students learn how commutator estimates in Schatten norms for the negative-energy spectral projection yield rate-explicit local and phase-space Weyl laws in Lp spaces even when the potential is only Holder-differentiable (class C1,1/2), and how these extend to mean-field interacting systems such as minimizers of the Hartree energy with singular Coulomb pair interactions.
Commutator Estimates and Quantitative Local Weyl’s Law for Schrödinger Operators with Non-Smooth
A study of semiclassical Schrodinger operators H = -h^2 Laplacian + V on L2(R^d) whose potential V is only of class C1,1/2 (once differentiable with Holder-1/2 derivative), rather than smooth. The au…