Quantum Mechanics 2

1. Time dependent perturbation theory.
2. Scattering theory.
3. Many body systems.
4. Relativistic quantum mechanics.

After successfully taking part in this module the students are able to:

1- Derive Fermi's golden rule and apply it to calculate transition probabilities,

2- Calculate the scattering amplitude and the differential cross-section in a scattering process,

3- Derive the optical theorem and understand its consequences,

4- Write-down the wave function of a system of bosons or fermions,

5- Calculate approximately the energy spectrum of an atom with many electrons,

6- Understand the formalism of "second quantization",

7- Derive the Klein-Gordon equation and the Dirac equation, and understand their consequences.

No prerequisites that are not already included in the prerequisites for the Master’s programmes.

The modul consists of a lecture and exercise classes.

In the thematically structured lecture the learning content is presented. With cross references between different topics the universal concepts in physics are shown. In scientific discussions the students are involved to stimulate their analytic-physics intellectual power.

In the exercise the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.

Blackboard, Script, slides if available

• C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics Vol. I and II, Wiley, 1977.
• Jun John Sakurai, Modern Quantum Mechanics, Benjamin/Cummings Publishing Company, 1985.
• A. Messiah, Quantum Mechanics I and II, Dover Publ. 1995 2nd edition.
• F. Schwabl, Advanced Quantum Mechanics, Springer-Verlag 2000 (third edition).
• Relativistic Quantum Mechanics, J.D. Bjorken, S.D. Drell, MC Graw Hill Book Company; 1st edition (1964)

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

• Calculate transition probabilities for a harmonic oscillator under a small time-dependent perturbation.
• Derive the selection rules and transition rates for a hydrogen atom under the influence of a radiation field.
• Calculate the phase shifts and the cross section for a non-relativistic particle scattering off a given potential.

In the exam no learning aids are permitted.

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of passing the voluntary test exam during the semester