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2021W, VU, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VU Lecture and Exercise
• Format: Hybrid

## Learning outcomes

After successful completion of the course, students are able to:

1) Identify relevant mathematical structures and concepts in condensed matter problems, e.g. eivenvectors, eigenvalues and other linear algebra structures, correlation functions, inital value and boundary value problem of differential equations, Fourier transform.

2) Use discrete and continuous symmetries to assess the correctness of numerical results and to simplify physical problems

3) Construct Fock space of fermionic problems and apply it to simple systems with few degrees of freedom

4) Use Fourier transforms both in space and time/frequency domain

5) Understand basic approximations used in condensed matter physics, e.g. strong and weak coupling expansion, large-N expansion, embedding, stochastic simulations

6) Calculate magnetic susceptibility of 6-site Hubbard molecule as a function of temperature

## Subject of course

Foundations of quantum theory: causal evolution and measurement, observables, wavefunctions, Hermitean operators, evolution operator and Hamiltonian

Schrodinger equation, stationary states, time evolution, Hemitean and unitary operators

Basic statistical physics, Boltzmann factor

Symmetry and eigenvalue degeneracy

Quantum theory of many particles: fermions and bosons, Pauli principle, commutation relations, Pauli principle

Lattice models, translational symmetry

Exact diagonalization, construction of Fock space and fermionic operators

Correlation functions and linear response to external perturbations

Non-interacting electrons in periodic solids, Bloch theorem

The concepts will be developed step by step on a pilot problem (6-site cluster). We will develop a code to calculate the discussed observables during the coure.

## Teaching methods

`Interactive handling of the course`

## Mode of examination

Oral

The format of course is prerecorded lectures + weekly discussion sessions (either online or in person)

The 'Vorbesprechung' will take place on October 4, 13:00 via zoom

https://tuwien.zoom.us/j/7478799034
Meeting ID: 747 879 9034

"Anmeldung" is required!

## Examination modalities

Presentation of simple numerical project and discussion of corresponding methods and physical concepts

## Course registration

Begin End Deregistration end
21.09.2021 12:00 11.10.2021 15:00 14.10.2021 12:00

## Curricula

Study CodeSemesterPrecon.Info
066 646 Computational Science and Engineering

## Literature

No lecture notes are available.

## Previous knowledge

basic linear algebra, basic programming

English