Advanced Theoretical Chemistry II

Many-Body Wavefunctions, Second Quantization, Coupled Cluster, Feynman Graphs
Ma-TC-A II


Contents

  1. Introduction

    • many-body wavefunctions
    • information carried by determinant

  2. 2nd quantization I: basic principles, idea

    • minimal representation: occupation number vectors
    • creators and annihilators: anti-commutation relations
    • function spanning and physical operators
    • size consistency: CI vs. coupled cluster (CC) ansatz
    • operator ranks

  3. 2nd quantization II: calculus

    • normal order
    • contractions
    • Wick's theorem (I) and (II)
    • particle/hole formalism
    • CC equations

  4. Feynman, Goldstone, Hugenholz diagrams

    • motivation, information, redundance, irrelevance
    • translation Algebra ↔ Diagram
    • elimination of remaining redundant information
    • Hamilton and cluster operators in diagrammatic form
    • contractions and CC equations in diagrammatic form


Notes

The lecture contents of TC-A in winter and summer terms differ. The winter term's subjects are more fundamental and basic.

If you are free (of scheduling issues) to choose I recommend attending the winter term's lecture. However, the summer term's lecture is self contained and may be attended independently. Both lectures are (offline) mostly black board type lectures. In the winter semester there is also a number of computer animated illustrations.

In any case you should have a theoretical interest and no reservations about math...

Many students before attended one term as TC-A and the other as S-module.

See also: TC-A I in the winter term


Organization

Lecture 3 SWS
Exercise 1 SWS
Exam written, open book

Further administrative information

University of Cologne

Theoretical Chemistry

Education

Workgroup Hanrath


Selected Animations