Master degree in Materials Science

Quantum Effects in Materials: From Theory to Modelling

Quantum Effects in Materials: From Theory to Modelling

Academic year 2023/2024

Sommario del corso

• Course objectives
• Results of learning outcomes
• Program
• Course delivery
• Learning assessment methods
• Suggested readings and bibliography
• Notes
• Class schedule
• Teaching tools
• Course card

Course objectives

Quantum mechanics is the branch of physics that describes the behaviour of subatomic particles such as electrons and protons. Many properties of matter emerge from effects that originate at the quantum scale, and specially those features that make materials interesting for advanced applications. Moreover, today’s quantum-chemical simulation techniques allow to exploit the power of modern computers to apply such theoretical tools to the routine study of molecules and materials.

The main objective of this course is to provide students with a complete understanding of basic and advanced principles of quantum mechanics, which are the prerequisite to a modern approach to materials chemistry and solid state physics. In addition to that, the course aims at discussing how these concepts can be applied to the study of real systems, the necessary approximations involved, and the formal aspects required to translate equations into computer algorithms.

Results of learning outcomes

• Master the language and formalisms of quantum mechanics.
• Know the main theoretical tools and techniques used to describe relevant effects taking place at the scale of electrons and nuclei.
• Understand the physics of light-matter interaction.
• Understand the equations and approximations implemented in modern quantum-chemical simulation softwares.
• Ability to properly set up, run and interpret the results of simple quantum chemical calculations of solids.
• Ability to understand the reliability of a quantum-chemical simulation based on approximations and parameter used.

Program

MODULE A: QUANTUM PHYSICS

• Review of basic concepts: fundamentals of quantum mechanics, linear algebra, bra/ket notation, probability theory.
• Quantum confinement effects: one-dimensional potential wells and tunnel effect. Applications to alpha decay phenomena and scanning-tunneling microscopy.  
• Angular momentum, spin and addition of angular momenta
• Motion of charged particles in electro-magnetic fields, gauge invariance, Landau levels and quantum Hall effect.
• Non-degenerate perturbation theory, fundamentals of degenerate perturbation theory, applications to hydrogen-like atoms (normal Zeeman effect, relativistic correction, spin-orbit correction, anomalous Zeeman effect, Stark effect).
• Time-dependent phenomena: time evolution, time-dependent perturbation theory, Fermi golden rule. Application to electronic transitions and lasers.
• Identical particles, bosons and fermions, exchange interactions.

MODULE B: QUANTUM CHEMISTRY AND MODELLING

• The many-electron problem: spinorbitals and Slater determinants.
• Molecular electronic structure: the molecular electrostatic Hamiltonian and the Hartree-Fock (HF) method. The self-consistent field procedure.
• Electron correlation. Basics of Density Functional Theory and post Hartree-Fock (configuration interaction, Moeller-Plesset) treatments.
• Electronic structure of ordered solids: Fourier transforms, band theory, Bloch theorem, Fermi level, periodic boundary conditions. Extension of HF and DFT computational methods to solids.
• Nuclear motion: geometry optimization, vibrational frequencies.
• Light-matter interaction. Electronic excitations, linear response, dielectric properties of matter, simulation of vibrational spectra. 

Course delivery

The course is delivered in the form of frontal face-to-face lectures, exercise sessions, and a final computational quantum chemistry laboratory

Learning assessment methods

• The exam consists in a written and an oral part for each module, both in person and mandatory.
• During ordinary exam sessions (Jan+Feb, Jun+Jul+Sep) exams for module A and for module B can be taken together or separately; if they are taken separately, the partial mark is kept only within the same exam session. For instance, if one passes module A in Jan, the mark is valid only until Feb; if one passes module B in Jun, the mark is kept ony until Sep.
• Within a given ordinary exam session, there is no ordering for the exams of the two modules, i.e. one can take module A first and module B after, or viceversa.
• Conversely, during extraordinary exam sessions (Apr, Nov) the exams for the two modules must be taken together.

• The written exam for module A (or B) lasts 1 hour. The joint written exam for modules A+B lasts 2 hours.
• The written exam consists in a set of multiple-choice questions + some open-ended questions.
• The oral exam consists in ‘theoretical’ questions aiming at ascertaining the understanding of the topics developed in class.

MODULE A

• Lecture notes
• F. Schwabl, Quantum Mechanics
• D. Griffiths, Introduction to Quantum Mechanics.
• J. J. Sakurai, Modern Quantum Mechanics

MODULE B

• Lecture notes
• Szabo, Ostlund, "Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory"

Notes

Class schedule

• Teaching material
• Exams and finals
• Class schedule
• Go to Moodle
• Register for the course
• Enrolled students
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