Spurious localized highest-frequency modes in Schr\"odinger-type equations solved by finite-difference methods
Abstract
High-frequency solutions of one or several Schr\"odinger-type equations are well known to differ very little from the plane wave solutions [ ik x]. That is, the potential terms impact the envelope of a high-frequency plane wave by only a small amount. However, when such equations are solved by a finite-difference method, the highest-frequency solutions may, under certain conditions, turn out to be localized. In this letter we explain this numerical artifact.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.