Code
Φ-703
Level
Graduate
Category
B
Teacher
N. Flytzanis
ECTS
6
Hours
6
Semester
Winter
Display
Yes
Offered
Yes
Teacher Webpage
Goal of the course
Objectives 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.
Program
Moday, 13:00-15:00, 2nd floor seminar room
Thursday, 12:00-14:00, 2nd floor seminar room
Thursday, 12:00-14:00, 2nd floor seminar room
Syllabus
Principles 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.
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.
Bibliography
1. 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".
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".
