High-Order Exponential Operator Splitting Methods for Time-Dependent Schrödinger Equations

Abstract

In this paper, we deduce high-order error bounds for exponential operator splitting methods. The employed techniques are specific to linear differential equations of the form $u'(t) = A \, u(t) + B \, u(t)$, $t \geq 0$, involving an unbounded operator A. In particular, evolutionary Schrödinger equations with sufficiently regular initial values are included in the analysis.