Advanced Quantum Mechanics

1. Time dependent Hamiltonian: interaction picture, two state problem, adiabatic approximation, Berry’s phase
2. Time dependent perturbation theory: review and applications
3. Atoms in electromagnetic fields: absorption and stimulated emission, multipole expansion (electric dipole, quadrupole, magnetic dipole), photoelectric effect
4. Atoms and quantum theory of radiation, spontaneous emission
5. Scattering theory: S Matrix and scattering amplitude, T matrix and Lippmann-Schwinger equation, optical theorem, Born Approximation, phase shifts and partial waves, eikonal approximation, scattering length, effective range and shallow bound states, resonances and bound states, parity and time reversal invariance, inelastic electron-atom scattering, form factors
6. systems of identical particles: two electron systems, helium atom scattering of identical particles

After successful completion of the 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. Calculate atomic transitions in presence of electromagnetic radiation
5. Analyse a scattering cross section in partial waves and calculate phase shifts
6. Calculate the cross section in presence of a resonance
7. Calculate the lifetime of an atomic state
8. Calculate transition rates at higher order in the multipole expansion

In the lecture the content will be explained, the theory will be constructed and examples and applications will be worked out. Discussion with students will be encouraged. The students will be guided through the literature.

In the exercises the students will be in small groups and the content of the exercises will be discussed together. In the exercise the learning content is deepened and understood using problem examples and calculations. Thus the students will be able to explain and apply the learned physics knowledge independently.

Blackboard/online (zoom) or slides presentation
accompanying informations on-line

1. A. Messiah, Quantenmechanik Bd. 1 und 2, de Gruyter 1991
2. A. Galindo and P. Pascual, Quantum Mechanics I und II, Springer 1990
3. F. Schwabl, Quantenmechanik, Springer 2007
4. F. Schwabl, Quantenmechanik für Fortgeschrittene, Springer 2008
5. G. Auletta, M. Fortunato and G. Parisi, Quantum Mechanics, Cambridge University Press 2009
6. M. Le Bellac, Quantum Physics, Cambridge University Press 2011
7. S. Weinberg, Lectures on Quantum Mechanics, Cambridge University Press 2015
8. C. Cohen-Tannoudji, B. Diu and Franck Laloë Quantenmechanik Bd. 1, 2 und 3, de Gruyter 2019
9. J.J. Sakurai and J. Napolitano, Modern Quantum Mechanics, Cambridge University Press 2020

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 a cross section for a scattering of a central potential.
• Calculate atomic multipole transitions in an electromagnetic field.
• Use partial wave expansion and calculate phase shift for a scattering on a potential.
• Discuss stimulated and spontaneous emission.
• Solve the Lippmann Schwinger equation.
• Solve a scattering problem using the Born approximation or the Eikomal approximation.
• Calculate properties of Helium atom.
• Using the effective range approximation in a scattering calculation.
• Calculate the cross section for a resonance.

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 both exam period directly following the lecture period and subject to the condition that the student passes the mid-term of passing the voluntary test exam during the semester