1204.2334 (Taras I. Lakoba)

Spurious localized highest-frequency modes in Schrödinger-type
equations solved by finite-difference methods    [PDF]

Taras I. Lakoba

High-frequency solutions of one or several Schr\"odinger-type equations are well known to differ very little from the plane wave solutions $\exp[\pm ik x]$. 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.

View original: http://arxiv.org/abs/1204.2334