Quantum Mechanics 2
Module PH1002 [ThPh KTA]
Module version of WS 2021/2 (current)
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
available module versions  

WS 2021/2  WS 2020/1  WS 2019/20  WS 2018/9  WS 2017/8  WS 2016/7  WS 2015/6  WS 2010/1 
Basic Information
PH1002 is a semester module in English or German language at Master’s level which is offered in winter semester.
This module description is valid to SS 2022.
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) 

300 h  90 h  10 CP 
Responsible coordinator of the module PH1002 is Antonio Vairo.
Content, Learning Outcome and Preconditions
Content
 Time dependent Hamiltonian
 Interaction picture
 Two state problem: spin magnetic resonance
 Adiabatic approximation
 Berry's phase
 Time dependent perturbation theory
 Dyson series and transition probabilities
 Constant and harmonic perturbation
 Fermi's golden rule
 Interaction with a classical radiation field: absorption and stimulated emission
 Electric dipole approximation
 Phase space and densitiy of states
 Interaction with a classical radiation field: photoelectric effect
 Interaction with a classical radiation field: spontaneous emission
 Scattering theory
 Scattering as time dependent perturbation
 T matrix and LippmannSchwinger equation
 Scattering amplitude
 Optical theorem
 Born approximation
 Phase shifts and partial waves
 Eikonal approximation
 Low energy scattering and resonances
 Low energy scattering and bound states
 Scattering length, effective range, shallow bound states
 Parity and time reversal invariance
 Inelastic electronatom scattering; form factors
 Open quantum systems
 Entangled states
 Density matrix
 Reduced density matrix
 von Neumann entropy
 Unitary evolution: von Neumann equation
 Evolution of the reduced density matrix: Lindblad equation
 Quantum cryptography and no cloning theorem
 Systems of identical particles
 Bosons and fermions
 Twoelectron system
 Helium atom
 Scattering of identical particles
 Multiparticle states
 Fock space and second quantization
 Fock space for bosons
 Fock space for fermions
 One particle and multiparticle operators
 Field operators
 Equation of motion
 Fermi energy and electron gas
 Quantization of the electromagnetic field
 Photons
 Casimir effect
 KleinGordon equation
 Derivation and solutions
 Hamilton, momentum, charge current operators in second quantization
 Dirac equation
 Derivation
 Dirac matrices
 Free particle solution
 Coupling to electromagnetism, Pauli equation, gyromagnetic ratio
 Quantized field
 Symmetries: Lorentz, C, P, T
 Solution of the Dirac equation in a central potential; energy spectrum of the hydrogen atom
Learning Outcome
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 crosssection in a scattering process,
3 Derive the optical theorem and understand its consequences,
4 Define entagled states. Define mixtures and pure states. Write the evolution equations for closed and open quantum systems,
5 Writedown the wave function of a system of bosons or fermions,
6 Writedown the KleinGordon and Dirac equations,
7 Calculate the Dirac energy spectrum for the hydrogen atom,
8 Understand the formalism of "second quantization",
9 Quantize the electromagnetic, KleinGordon and Dirac field operators
Preconditions
No prerequisites that are not already included in the prerequisites for the Master’s programmes.
Courses, Learning and Teaching Methods and Literature
Learning and Teaching Methods
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 analyticphysics 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.
Media
Blackboard/online (Zoom), Script, slides if available
Literature

C. Itzykson and J.B. Zuber,
Quantum Field Theory,
McGrawHill 1980
R.P. Feynman, Feynman Vorlesungen über Physik Bd. 3, Oldenbourg Wissenschaftsverlag 1999
S. Flügge, Practical Quantum Mechanics, Springer 1999
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 transition probabilities for a harmonic oscillator under a small timedependent 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 nonrelativistic 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 both exam period directly following the lecture period and subject to the condition that the student passes the midterm of of obtaining 60% of the total points of the problem sets.
Exam Repetition
The exam may be repeated at the end of the semester.