A remark on the absence of eigenvalues in continuous spectra for discrete Schr\"odinger operators on periodic lattices
Abstract
We prove a Rellich-Vekua type theorem for Schr\"odinger operators with exponentially decreasing potentials on a class of lattices including square, triangular, hexagonal lattices and their ladders. We also discuss the unique continuation theorem and the non-existence of eigenvalues embedded in the continuous spectrum.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.