# Tensor product approximation and numerical solution of the electronic Schrödinger equation

## John von Neumann Gastvorlesung (Dozent Prof. Dr. Reinhold Schneider ^{})

## Place and Time

- Time: Di, Mi, 16:00 - 18:00, Start: April 17th
- Place: Di: 02.08.011 (Seminarraum M2/M3), Mi: 02.04.011 (Seminarraum M9/M10)

## Contents

- In the first part of the lecture, we will consider the approximation of multi-variate functions by tensor products. We are aiming an appropriate generalization of the famous results by E. Schmidt about low rank factorization from two to arbitrary dimensions. After a short introduction we will focus on the relatively new approach of Hierarchical Tucker representation. Next we will consider partial differential equations in high dimensions and focus afterwards on the electronic Schrödinger equation and their numerical treatment by wave function approaches. Therein, we will discuss Full CI, Hartree Fock and multi-configuration approaches. We will consider the Coupled Cluster method in more detail, the QC- DMRG algorithm and matrix product states and its connection to the first part of the lecture.

## Slides (Lecture)

- Introduction
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7
- Lecture 8
- Lecture 9

## Slides (Colloquium)

## Slides (Talk Max-Planck Institute)

## Literature

- Helgaker et al.: Molecular electronic structure theory Landsberg: Geometry of Tensor products.

## Links:

## Contact/Consultation Hour:

- Prof. Dr. Reinhold Schneider, Room 03.10.058, Consultation hour: N.N.