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Quantum Mechanics of Molecular Systems

Module PH2165

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2013

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

available module versions
WS 2019/20WS 2018/9WS 2017/8SS 2013

Basic Information

PH2165 is a semester module in German or English language at Master’s level which is offered irregular.

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 Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 75 h 5 CP

Responsible coordinator of the module PH2165 in the version of SS 2013 was Philipp Scherer.

Content, Learning Outcome and Preconditions

Content

Schrödinger equation and wavefunctions

particle in a box
harmonic oscillator
anharmonic corrections
rigid rotor

molecular states

Born-Oppenheimer approximation

Slater-determinants
electron structure calculations for molecular systems (LCAO-MO)

electron-vibration coupling


transitions between states,

semiclassical curve crossing

Landau-Zener 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 Pi-electron 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 Born-Oppenheimer 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 electron-vibration coupling

Preconditions

basic quantum mechanics

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

lecture-style mediation of knowledge

interactive applets visualizing functional dependencies (individual sudies)

extra materials for more details (individual studies)

Media

blackboard

laptop/projector

lecture notes

Java applets

extra material (additional notes)

Literature

P.O.J. Scherer, S.F. Fischer Theoretical Molecular Biophysics

Haken, Wolf Molekülphysik und Quantenchemie

Schwabl, quantum mechanics

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:

  • to describe Pi-electron systems of molecules 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 Born-Oppenheimer 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 electron-vibration coupling

Exam Repetition

The exam may be repeated at the end of the semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
TimeLocationInfoRegistration
Exam in Quantum Mechanics of Molecular Systems
Mon, 2020-02-03 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin vor Mo, 23.03.2020. // Dummy date. Contact examiner for individual appointment. Registration for exam date before Mon, 2020-03-23. till 2020-01-15 (cancelation of registration till 2020-02-02)
Tue, 2020-03-24 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin zwischen Di, 24.03.2020 und Sa, 18.04.2020. // Dummy date. Contact examiner for individual appointment. Registration for exam date between Tue, 2020-03-24 and Sat, 2020-04-18. till 2020-03-23
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