Quantum Mechanics of Molecular Systems
Module PH2165
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  SS 2013 
Basic Information
PH2165 is a semester module in English language at Master’s level which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
 Specific catalogue of special courses for Biophysics
 Complementary catalogue of special courses for condensed matter physics
 Complementary catalogue of special courses for nuclear, particle, and astrophysics
 Complementary catalogue of special courses for Applied and Engineering Physics
 Specialization Modules in EliteMaster Program Theoretical and Mathematical Physics (TMP)
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 PH2165 is Philipp Scherer.
Content, Learning Outcome and Preconditions
Content
Schrödinger equation and wavefunctions
particle in a box
harmonic oscillator
anharmonic corrections
rigid rotor
molecular states
BornOppenheimer approximation
Slaterdeterminants
electron structure calculations for molecular systems (LCAOMO)
electronvibration coupling
transitions between states,
semiclassical curve crossing
LandauZener model
time dependent perturbation theory
Fermi's golden rule
optical transitions
Learning Outcome
After participating, the students are able to apply simple quantum mechanical models to molecular systems to analyse molecular states and transitions.
They are able
 to describe Pielectron systems of molecules with conjugated double bonds within the free electron model
 to formulate the Hamiltonian of a harmonic oscillator with ladder operators and to solve the time independent Schrödinger equation
 describe anharmonic effects with perturbation theory
 determine localized wave packets which solve the time dependent Schrödinger equation for free particles and particles in a harmonic potential
 to formulate the Hamiltonian of a molecular system and to apply the BornOppenheimer approximation to separate the motion of electrons and nuclei
 to describe the ground state of a many electron system with a Slater determinant
 to describe modern electron structure methods
 to apply the quasiclassical approximation to molecular transitions and to derive the Landau Zener rate expression with perturbation theory
 to derive the rate expression for molecular transitions into a continuum of final states and to apply it to optical transitions
 to interpret optical spectra of larger molecules on the basis of electronvibration coupling
Preconditions
basic quantum mechanics of Bachelor level
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Type  SWS  Title  Lecturer(s)  Dates  Links 

VO  2  Quantum Mechanics of Molecular Systems  Scherer, P. 
Thu, 10:00–12:00, PH 2271 

UE  2  Exercise to Quantum Mechanics of Molecular Systems  Scherer, P.  dates in groups 
Learning and Teaching Methods
The module consists a lecture and exercises.
During the lecture the learning content is presented. Necessary mathematical methods are explained and important theoretical results are derived explicitly. Functional relationships are shown with graphics and computer examples. Theoretical results are compared with experimental data from the literature with the help of computer presentations. After the lecture there is time for discussion.
Numerous problem examples with solutions deepen the learning content in the exercises. Here the mathematical derivations are discussed in more detail and their application is exercised using selected problem examples and calculations. Thus the students are able to explain and apply the learned knowledge on their own.
A series of interactive applets are introduced in the lecture and serve for individual studies visualizing functional relationships and the dependency of the theoretical results on the relevant parameters
additional notes and literature references are provided for further deepening of the learning content
Media
Blackboard, laptop/projector, lecture notes, exercises and examples, Java programs, extra material (additional notes)
Literature
 P.O.J. Scherer & S.F. Fischer: Theoretical Molecular Biophysics, SpringerVerlag, (2017)
 H. Haken & H. Wolf: Molekülphysik und Quantenchemie, SpringerVerlag, (2006)
 F. Schwabl: Quantenmechanik, SpringerVerlag, (2007)
 Lecture notes
Module Exam
Description of exams and course work
There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.
For example an assignment in the exam might be:
 describe the Pielectron system of a molecule with conjugated double bonds within the free electron model
 formulate the Hamiltonian of a harmonic oscillator with ladder operators and to solve the time independent Schrödinger equation
 describe anharmonic effects with perturbation theory
 determine localized wave packets which solve the time dependent Schrödinger equation for free particles and particles in a harmonic potential
 formulate the Hamiltonian of a molecular system and to apply the BornOppenheimer approximation
 describe the ground state wavefunction of a many electron system
 describe modern electron structure methods
 apply the semiclassical approximation to molecular transitions and derive the Landau Zener rate expression with perturbation theory
 derive the rate expression for molecular transitions into a continuum of final states and apply it to optical transitions
 interpret optical spectra of larger molecules on the basis of electronvibration coupling
Remarks on associated module exams
The exam for this module can be taken together with the exam to the associated followup module PH2187: Elementary Processes in Molecular Systems / Elementare Prozesse in molekularen Systemen after the follwoing semester. In this case you need to register for both exams in the following semester.
Exam Repetition
The exam may be repeated at the end of the semester. There is a possibility to take the exam in the following semester.