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Theoretische Chemie I: Einführung in die Quantenmechanik

General information:

Module description (PDF in German)

Organizational information,  summer term 2021 (SoSe 2021):

Please refer to the internal Moodle Web site of the course for assignments, exercises and lecture notes.
Registration key for the SoSe 2021: <TCI>(2021)

Lecturer:   Prof. Dr. Oriol Vendrell
Exercises coordination:   Prof. Dr. Oriol Vendrell
Tutor:   t.b.d.

The usual development of this course is through regular blackboard lectures (2 SWS) and exercises (2 SWS) on a weekly basis. This semester, due to the corona-situation, the course is taking place online in an asynchronous format. This means, for each block the following working materials will be indicated on the Moodle page of the course:

  • Reading material from the main book (Griffiths) and, if meaningful, from other books.
  • Hand-written notes, which correspond to what would have been developed on the blackboard.
  • Video and/or audio material discussing the corresponding topics.
  • Exercises from the booklet and, when meaningful, from the main textbook.

Blocks last usually more than a week, often about two weeks. New materials will be provided at the beginning of each week and the proposed exercises at the beginning of week X will be discussed by the tutors towards the middle/end of week X+1, thus providing time to digest the corresponding theory.

Overview of lecture contents:

(These contents serve as orientation and the order of presentation and exact list of topics discussed may slightly vary across semesters. Please refer to the internal Moodle web page of the course for further details.)

Block 1: Intro to QM concepts

- The wavefunction and its equation of motion, the Schrödinger equation
- Operators and the representation of observable quantities
- Quantum mechanical measurements and expectation values
- Conservation laws, time dependence of observable quantities. Ehrenfest and virial theorems.

Block 2: Formalism

- Hermitian operators and their properties
- Simultaneous eigenstates
- The generalized uncertainty principle
- Vectors in Hilbert space, Dirac's notation and matrix formulation of QM
- Changes of representation and linear transformations

Block 3: Linear motion

- The free particle
- Particle in a box: the emergence of quantization and boundary conditions
- The harmonic oscillator: eigenstates and eigenenergies
- Raising and lowering operators for the harmonic oscillator

Block 4: Circular motion and angular momentum

- Particle on a ring and its angular momentum
- Formal aspects of angular momentum algebra
- Orbital and spin-1/2 angular momenta
- Angular momentum of composite systems

Block 5: Methods of approximation

- Time-independent perturbation theory
- First-order time-dependent perturbation theory and Fermi's golden rule.
- Application to particle in an external electric field

Block 6: Quantum mechanics in Chemistry

- Wavefunctions of many-electron systems
- Applications to helium and molecular hydrogen

Recommended bibliography

Main textbook:

Other textbooks:

Online resources

Latest Revision: 2021-03-30
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