Multidimensional Periodic Schrödinger Operator

Focusing on the multidimensional Schrödinger operator with periodic potential, this book delves into both direct and inverse problems relevant to perturbation theory and spectral invariants. It offers detailed derivations of asymptotic formulas for Bloch eigenvalues and functions, while also constructing iso-energetic surface measures in high-energy contexts. A unique method validates the Bethe-Sommerfeld conjecture across dimensions and lattices, enabling the determination of spectral invariants from Bloch eigenvalues. An updated chapter addresses lower-dimensional cases, enriching the foundational understanding for subsequent discussions.