Quantenmechanik molekularer Systeme

What it is about

In the module you will learn to apply quantum mechanical models to molecular systems to describe states and transitions. By the end you will be able to analyze, for example, pi-electron systems, harmonic and anharmonic vibrations, Born–Oppenheimer separation, as well as simple many-electron descriptions and transition rates for optical processes.

What you will be able to do

Describe pi-electron systems of conjugated molecules in the free-electron model
Formulate the Hamiltonian of the harmonic oscillator with ladder operators and solve the time-independent Schrödinger equation
Describe anharmonic effects using perturbation theory
Determine localized wave packets for free particles and in the harmonic potential
Set up the Hamiltonian for molecular systems and apply the Born–Oppenheimer approximation
Describe the ground state of a many-electron system with a Slater determinant
Describe modern electronic structure calculations
Apply quasi-classical approximations to molecular transitions and derive the Landau–Zener expression
Derive a rate expression for transitions into a continuum (Fermi's Golden Rule) and apply it to optical transitions
Interpret optical spectra of large molecules in the context of electron–vibration interaction

What the module consists of

VorlesungExplanation of mathematical methods, derivation of key results, visualization with graphics and sample programs, comparison with literature findings
Übungdetailed discussion of derivations and practice problems applying what has been learned

Teaching method

Tafelanschrieb/Beamer/Skriptfor presentation and derivation of theoretical results
Grafiken und Beispielprogrammeto illustrate functional relationships
Computerpräsentationento compare theoretical results with experimental findings from the literature
Interaktive Appletsfor independent visualization and investigation of parameter-dependent relationships
Übungsaufgabento practice and understand the derivations and applications

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