35426 - Chemical Physics of Solid Materials M

Learning outcomes

At the end of the course, the student knows basic concepts, mathematical  structure and computational methods of quantum mechanics, necessary for the theoretical study of atoms, molecules and solid state systems. Moreover, the student learns to use quantum mechanics for studying electronic properties of atoms, molecules and crystals,  roto-vibrational properties of molecules, and the use of simple models for the electronic transport in nanoelectronic devices.

Course contents

Prerequisites: knowledges of classical physics, differential and integral calculus, linear algebra and general chemistry, given by the triennium courses, are requested. It is useful to have also elementary knowledges of Hamiltonian formalism and Maxwell electromagnetism. 

Suggestion: it is useful to follow also the Couse of Solid State Physical Chemistry.

Program:

• BASIC QUANTUM MECHANICS:  Postulates and fundamental concepts - Measurements of observables - Mathematical formalism - Symmetry and angular momenta - Matrix quantum mechanics - Wave mechanics in position and momentum representations - Time-independent Schroedinger equation - Time evolution of quantum states: time-dependent Schroedinger equation.

• QUANTUM-MECHANICAL METHODS: variational methods: Hartree-Fock, Configuration Interaction, Density Functional Theory - Perturbative Methods.

• MOLECULAR QUANTUM MECHANICS:  Born-Oppenheimer approximation - Molecular Orbital Theory - Valence Bond Theory - Calculation of electronic energies and stationary states of atoms and molecules - Calculation of roto-vibrational energies and states of molecules.

• ELEMENTS OF SOLID STATE PHYSICS:  Geometrical description of crystals: simple and composite lattices, Bravais lattices; primitive and unitary cells, Wigner-Seitz cells. Reciprocal lattices: definitions and basic properties; planes and directions in Bravais lattices; Brillouin zones. Translational symmetry in quantum-mechanical: Bloch theorem and electronic wavefunctions, bands and density of states; cyclic boundary conditions. 

• ELECTRONIC TRANSPORT IN NANODEVICES:  Modelling of a nanoscale transistor - An atomistic view of the electrical resistence - Energy levels diagram - Flow of electrons and rate equations - Current in one-level channel - The quantum of conductance.  The quantum theory of transport developed in the Course will be tested using a software for buiding/simulating electronic nanodevices. 

Readings/Bibliography

Attendance at lectures is very useful, the use of lecture notes and other material provided by the teacher is also very useful. For further investigation of the lecture items, the following books are suggested:

• J.J. Sakurai, Modern Quantum Mechanics, ed. Wiley.
• G.Grosso and G.Pastori Parravicini, Solid State Physics, ed. Academic Press.
• S.Datta, Quantum Transport. Atom to Transistors, ed. Cambridge.

Teaching methods

The course is organized in frontal lectures, where basic concepts, fundamental principles and mathematical techniques of quantum mechanics and solid state physics are presented and explained together with elements of quantum theory of charge transport. After the theoretical explanation of each subject,  lections will be devoted to the solution of exercises and specific problems involving prototype atomic, molecular and solid state systems, and simple models of nanoelectronic devices.  This procedure aims to aid the student in acquiring the ability to convert a physical problem into a theoretical-computational procedure able to give quantitative results.

Assessment methods

The learning assessment realizes through periodic exercises and a final test, that verifies the achievement of the following teaching targets:
-  knowledge of basic concepts, mathematical structure and computational methods of quantum mechanics and solid state physics;
-  ability of using the acquired theoretical tools to formulate and solve simple problems concerning atomic, molecular, and solid state systems. The final exam is oral, and based on questions on  the main items of the Course.

 

Teaching tools

Lecture notes and other didactic material are made available in electronic format. Attending also to the Solid State Physical Chemistry Course is suggested.

Office hours

See the website of Renato Colle