Courses Catalogue

Syllabus of the course: Applied Quantum Mechanics


In this web page we provide the syllabus of the course Applied Quantum Mechanics, offered by the Department of Physics.
The list of the courses offered during the current accademic year is available here.
The list of all courses offered by the Department of Physics is available here.

CodeΦ-703
TypeB
ECTS6
Hours6
SemesterWinter
InstructorN. Flytzanis
ProgramModay, 12:00-14:00, 2nd floor seminar room
Thursday, 12:00-14:00, 2nd floor seminar room
Web page
Goal of the courseObjectives of the course: Course is planned for 1st year graduate and 4th year undergraduate students. It starts with an intensive review of Quantum Mechanics and its application to problems that can be of interest to microelectronics or optoelectronics. The emphasis is in understanding the basic properties of the physical system and description in the language of quantum mechanics. Prerequisites: The course is designed for students in Physics but also with Engineering background. While the basic Q.M. is covered , previous knowledge of Quantum Mechanics or Solid State physics and Mathematics is very useful.
SyllabusPrinciples of Quantum Mechanics. Schrodinger equation and uncertainty principle. Operators and observables. Pauli principle. Wavepackets.
Free electron density of states in 1d, 2d, 3d and extension to quantum dots, wires and wells. One dimensional problems, transmission and tunneling. Scattering matrix and transfer matrix. LCAO approximation and application to two level systems and coupled well 1d systems. Periodic potential and Bloch states. Bands, effective mass, holes. Density of states.
Harmonic oscillator , spectrum and eigenstates. Creation and destruction operators. Application to electromagnetic wave quantization and coupled oscillators (phonons).
Angular momentum, spin and coupling. Spherical potential and application to spherical quantum dot. Hydrogen atom, spectrum and eigenstates.
Periodic table and polyelectronic atoms (screening, Hund rules). Mean field e-e interaction (Hartree). WKB Method. Time independent perturbation theory. Applications to the Hydrogen atom, spin-orbit etc. Applications like Stark phenomenon, Zeeman effect, k.p perturbation in solids etc. Variational method. Application to He atom, exchange energy. Discussion of Hartree-Fock method.
LCAO and molecules with application to hydrogen molecule. Hybridization (Si). Vibration and rotation of molecules.
Scattering and Born approximation. Applications in impurity scattering etc.
Time dependent perturbation. Golden Fermi rule, transition rates, spontaneous emission, Einstein relations.
Systems in equilibrium (electrons, photons, …). Electrons and holes in semiconductors.
Electrons in tetrahedral semiconductors.
Electron in electromagnetic field. Light matter interaction. Absorption coefficient, dielectric constant, excitons.
Out of Equilibrium, transport phenomena, Boltzmann equation in the relaxation time approximation. Conductivity in metals and non-degenerate semiconductors, mobility.
Bibliography1. Notes Ν. Flytzanis
2. A. F. Levi, Applied Quantum Mechanics, Cambridge.
3. A. Yariv, "Theory and Applications of Quantum Mechanics".
4. K. F. Brennan, " The Physics of Semiconductors with Applications to Optoelectronic Devices".

University of Crete - Department of Physics - P.O Box 2208 - GR-71003 Heraklion, Greece
phone: +30 2810 394300 - fax: +30 2810 394301