Textbook in PDF format Motivation Splitting methods for discretized Schrödinger equations Splitting methods for Hamiltonian systems Advantages of splitting methods and topics of this lecture Splitting methods for ordinary differential equations Preliminaries Symmetric methods Order of splitting and composition methods Splitting methods for linear Schrödinger equations The linear Schrödinger equation Splitting methods Error analysis for the space discretization Semigroup theory, part Abstract error analysis Application to the linear Schrödinger equation Splitting methods for nonlinear Schrödinger equations Problem setting and main results Stability: Proof of Proposition Local error in H1 (T): Proof of Proposition Local error in L2 (T): Sketch of the proof of Proposition Global error: Proof of Theorem Dimension splitting methods for parabolic problems Dimension splitting methods Semigroup theory, part Analytic setting Error analysis Gronwall’s lemma Sobolev spaces