The student
- will learn and understand methods and techniques at the heart of numerical calculations of the electronic structure in condensed-matter physics;
- will have the possibility to practice the theory learn, during practical computer sessions that are an integral part of the course and of the exam;
- will be able to choose the best solution for dealing with complex problems that may be encountered in the future career;
- will acquire a solid basis of computational and physical knowledge for future learning and development activities.

Basic knowledge of Quantum Mechanics, of Fortran or C programming, of an operating system (preferably Linux).

1. Variational method: expansion on a set of basis functions, secular problem, eigenvalues and eigenvectors. Examples: gaussian basis, plane-wave basis.
2. Hartree-Fock equations, self-consistent field. Examples of numerical solution of electronic states in molecules with a Gaussian basis set.
3. Electronic states in solids: solution of the Schroedinger equation for periodic potentials; pseudopotentials and plane waves.
4. Introduction to Density-Functional Theory and to the plane-wave pseudopotential method. Self-consistency, total energies, forces, first-principle molecular dynamics.

1) Lecture notes 2) J. M. Thijssen, Computational Physics (Cambridge, 1999)

.

The course is organized as a series of theoretical lessons in which the physical problems and the numerical concepts needed for their resolution are presented, followed by practical sessions in which examples of implementatation for specific simple problems are presented. The student will learn to use the concepts and to practise scientific programming by modifying and extending the examples presented during the course. In the second half of the course a software frequently used in research will be introduced

https://physicslab.uniud.it/persone/paolo-giannozzi/metodi-numerici-per-la-struttura-elettronica

The exam has a practical and an oral part. The practical part is a personal project consisting in the numerical solution of a problem, typically an extension of a problem encountered during the course. The oral part consists in the discussion of the written report on the project and of at least another subject of the course. The final mark reflects the quality of the numerical solution, of the written report, and of the oral exams.

0