Advanced Theoretical Chemistry I

Linear Algebra, Quantum Mechanics, Approximations, Many Particles

Dates and Locations (Winter Term 2023/24)

Lecture Monday, 11:00-12:30
except first on October 9th: 12:00-13:30
Friday, 12:00-12:45 expt. Sem 1
Exercise Friday, 10:00-10:45 expt. Sem 1

The lecture starts in the first week of lecture period, that is October 9th, 12:00, HS II.


Lecture 3 SWS
Exercise 1 SWS
Exam written, open book

Further administrative information


  1. Quantum mechanics I: experiments

    • spin sorting machine, double slit
    • fail of classical physics

  2. Linear algebra

    • group, field, linear space, scalar product, function space
    • (vector) representations, approximations, Fourier transformation
    • operators, operator representations
    • eigen basis, eigenfunction approximation, variance
    • matrices and operators
    • linear transformations: mirror, rotation, scale, shere, SO(3), O(3)

  3. Quantum mechanics II: mathematical description

    • postulates, time propagation (Schrödinger equation)
    • measurement projection, eigenfunction expansion, expectation value
    • spin, SU(2)

  4. Many body systems

    • particle types, product ansatz, anti-symmetry
    • configuration interaction (CI)
    • 1- and 2-density(matrices)
    • Hartree-Fock (HF)
    • density functional theory


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 II in the summer term

University of Cologne

Theoretical Chemistry


Workgroup Hanrath

Selected Animations