Proper orthogonal decomposition method for Schrödinger equation

Abstract

In this paper we consider the proper orthogonal decomposition (POD) method for one-dimensional Schrödinger equation. We begin of the review of basic ideas of POD. Later this method is applied to study the linear Schrödinger equation. The generation of optimal basis using POD and model reduction questions are discussed. Also the errors between the POD approximate solutions and the exact problems solutions are calculated. The results of two numerical examples for standing and travelling Gaussian wave are presented and analyzed.

Keywords

• one-dimensional Schrödinger equation
• numerical methods
• proper orthogonal decomposition method