Non-Self-Adjoint Schrödinger Operator with a Periodic Potential: Spectral Theories for Scalar and Vectorial Cases and Their Generalizations

This book offers a comprehensive exploration of spectral theory for non-self-adjoint differential operators with complex-valued periodic coefficients, addressing one of the most challenging problems in mathematical physics and quantum mechanics: constructing spectral expansions in the absence of a general spectral theorem. It examines scalar and vector Schrödinger operators, including those with PT-symmetric periodic optical potentials, and extends these methodologies to higher-order operat...