# 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.

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 2020/1 | WS 2019/20 | WS 2018/9 | WS 2017/8 | SS 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 workload | Contact hours | Credits (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

Type | SWS | Title | Lecturer(s) | Dates | Links |
---|---|---|---|---|---|

VO | 2 | Quantum Mechanics of Molecular Systems | Scherer, P. |
Thu, 10:00–12:00 |
eLearning documents |

UE | 2 | Exercise to Quantum Mechanics of Molecular Systems | Scherer, P. | dates in groups |

#### 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.