Course program
- The limits of classical physics
Brief review of Newtonian mechanics and classical electromagnetism. Black Body radiation, heat capacity of solids, photoelectric effect, Compton scattering. Wave aspects of particles: De Broglie hypothesis, scattering of electrons from a crystal. Hydrogen atom and the Bohr model.
- Operators
Mathematical properties of operators, eigenfunctions and eigenvalues of operators. Hermitian operators, orthogonality of the eigenfunctions of a Hermitian operator, normalization and completeness of eigenfunctions. Hermitian adjoint operators. Dirac notation.
- The Basic postulates of Quantum Mechanics
Average value of an observable, commutation relation for the momentum and position operators, Commuting operators and their eigenfunctions. Significance of the state wave function. Gaussian wavepackets. Eigenfunctions of the energy operator, the time independent Schrodinger equation.
The uncertainty principle. Examples.
- One-dimensional energy eigenvalues problems
Infinite potential well, finite potential well, finite potential barrier. Quantum tunneling. The harmonic oscillator, creation and annihilation operators.
- Spin angular momentum
The Stern-Gerlach experiment, Spin ½ systems, Spin operators and commutation relations. Pauli two-component formalism. Pure and mixed states.
- Matrix formulation of Quantum Mechanics
Some Basic Matrix properties, matrix diagonalization, representations of operators as matrices, deriving eigenfunctions and eigenvalues of an operator by the matrix method.
- The Quantum Mechanics of angular momentum
Angular momentum operators, eigenfunctions and eigenvalues, spherical harmonics. Matrix elements of the angular momentum operators, addition of angular momenta. Particles in spherical symmetric potential fields, the hydrogen atom. Introduction to time independent perturbation theory.
- Basic concepts of statistical mechanics
Phase space, Boltzmann, Fermi-Dirac and Bose-Einstein distributions. Examples.
Prerequisites
It is useful to have basic knowledge in mathematics, classical physics and chemistry.
Books
A. Yariv, “An Introduction to Theory and Applications of Quantum Mechanics”, DOVER
N. Zettili, “Quantum Mechanics: Concepts and Applications”, Wiley
J.J Sakurai, “Modern Quantum Mechanics” Addison Wesley
D.J. Griffiths, “Introduction to Quantum Mechanics” Cambridge University Press
Teaching mode
Lectures and exercises in the classroom. Homeworks
Exam mode
Intermediate written exam on the topics of the first module composed of 4 open questions about theory to evaluate the knowledge and understanding of basic concepts (20% of the total grade) and one numerical exercise to evaluate the ability to apply the acquired knowledge to specific problems (10 %).
Intermediate written exam on the topics of condensed matter physics (see second module description for details) will contribute for 30% of the total grade
Final oral exam ( 40% of the total grade):
- discussion of both intermediate tests in to evaluate the knowledge and understanding ability of the students to judge and correct their mistakes by improving the knowledge autonomously.
- Verification of the ability to apply the acquired knowledge in the field of modern physics to the most common nanoscale phenomena.
- Verification on language property and clarity of presentation
Lesson mode
Lectures and exercises in the classroom. Homeworks
