Advanced Quantum Mechanics
Module PH0024 [QM*]
Basic Information
PH0024 is a semester module in German language at Bachelor’s level which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
 Theory courses for nuclear, particle, and astrophysics
If not stated otherwise for export to a nonphysics program the student workload is given in the following table.
Total workload  Contact hours  Credits (ECTS) 

150 h  60 h  5 CP 
Responsible coordinator of the module PH0024 is Nora Brambilla.
Content, Learning Outcome and Preconditions
Content
 Time dependent Hamiltonian: interaction picture, two state problem, adiabatic approximation, Berry’s phase
 Time dependent perturbation theory: review and applications
 Atoms in electromagnetic fields: absorption and stimulated emission, multipole expansion (electric dipole, quadrupole, magnetic dipole), photoelectric effect
 Atoms and quantum theory of radiation, spontaneous emission
 Scattering theory: S Matrix and scattering amplitude, T matrix and LippmannSchwinger 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 electronatom scattering, form factors
 systems of identical particles: two electron systems, helium atom scattering of identical particles
Learning Outcome
After successful completion of the module the students are able to:
 Derive Fermi's golden rule and apply it to calculate transition probabilities
 Calculate the scattering amplitude and the differential crosssection in a scattering process
 Derive the optical theorem and understand its consequences
 Calculate atomic transitions in presence of electromagnetic radiation
 Analyse a scattering cross section in partial waves and calculate phase shifts
 Calculate the cross section in presence of a resonance
 Calculate the lifetime of an atomic state
 Calculate transition rates at higher order in the multipole expansion
Preconditions
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Type  SWS  Title  Lecturer(s)  Dates  Links 

VO  2  Advanced Quantum Mechanics  Brambilla, N. 
Mon, 10:00–12:00, PH HS2 

UE  2  Exercise to Advanced Quantum Mechanics 
Mohapatra, A.
Säppi, S.
Responsible/Coordination: Brambilla, N. 
singular or moved dates and dates in groups 
Learning and Teaching Methods
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.
Media
Blackboard/online (zoom) or slides presentation
accompanying informations online
Literature
 A. Messiah, Quantenmechanik Bd. 1 und 2, de Gruyter 1991
 A. Galindo and P. Pascual, Quantum Mechanics I und II, Springer 1990
 F. Schwabl, Quantenmechanik, Springer 2007
 F. Schwabl, Quantenmechanik für Fortgeschrittene, Springer 2008
 G. Auletta, M. Fortunato and G. Parisi, Quantum Mechanics, Cambridge University Press 2009
 M. Le Bellac, Quantum Physics, Cambridge University Press 2011
 S. Weinberg, Lectures on Quantum Mechanics, Cambridge University Press 2015
 C. CohenTannoudji, B. Diu and Franck Laloë Quantenmechanik Bd. 1, 2 und 3, de Gruyter 2019
 J.J. Sakurai and J. Napolitano, Modern Quantum Mechanics, Cambridge University Press 2020
Module Exam
Description of exams and course work
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 midterm of passing the voluntary test exam during the semester
Exam Repetition
The exam may be repeated at the end of the semester.