Code
Φ-305
Level
Undergraduate
Category
B
Teacher
V. Niarchos
ECTS
6
Hours
4
Semester
Spring
Display
Yes
Offered
Yes
Teacher Webpage
Goal of the course
This elective course is a continuation of the compulsory Quantum Mechanics course. Its goal is to cover the remaining basic concepts of quantum mechanics in an undergraduate level. It is addressed to students who wish to continue their studies in modern topics of theoretical and experimental physics.
Program
Thursday, 15:00-17:00, Amphitheater ST
Friday, 11:00-13:00, Amphitheater ST
Friday, 11:00-13:00, Amphitheater ST
Syllabus
Fast review of basic Quantum mechanics, (1 week)
Introduction to perturbation theory: Types of perturbations and general methodology.Simple time-independent non-degenerate perturbation theory. Degenerate perturbation theory. Variational methods. Spin-orbit coupling in hydrogen-like atoms, magnetic electron proton interaction and hyperfine splitting. (Trahanas, Chapters 9-10, 3 weeks)
Scattering Theory. One-dimensional scattering, differential cross section, approximate calculation of the scattering amplitudes, Born approximation, three-dimensional problems, scattering of identical particles. (Trahanas, Chapter 11, 2 weeks)
Time-dependent perturbation theory and quantum transitions. Discrete spectrum, Fermi’s rule, applications, Rabi oscillations, interactions of atoms and light, dipole approximation, ionization, electrons in a magnetic field, Aharonov-Bohm effect.(Trahanas, Chapters 12-13, 4 weeks)
Density matrix and applications to thermal ensembles and two-level systems.(Trahanas, Chapter 4, 1 week)
Entangled states, Bell’s inequalities, entangled photons. States of maximal entanglement, entanglement entropy, quantum teleportation and quantum cryptography. (mainly from Trahanas, Chapters 14-15, 2 weeks)
Introduction to perturbation theory: Types of perturbations and general methodology.Simple time-independent non-degenerate perturbation theory. Degenerate perturbation theory. Variational methods. Spin-orbit coupling in hydrogen-like atoms, magnetic electron proton interaction and hyperfine splitting. (Trahanas, Chapters 9-10, 3 weeks)
Scattering Theory. One-dimensional scattering, differential cross section, approximate calculation of the scattering amplitudes, Born approximation, three-dimensional problems, scattering of identical particles. (Trahanas, Chapter 11, 2 weeks)
Time-dependent perturbation theory and quantum transitions. Discrete spectrum, Fermi’s rule, applications, Rabi oscillations, interactions of atoms and light, dipole approximation, ionization, electrons in a magnetic field, Aharonov-Bohm effect.(Trahanas, Chapters 12-13, 4 weeks)
Density matrix and applications to thermal ensembles and two-level systems.(Trahanas, Chapter 4, 1 week)
Entangled states, Bell’s inequalities, entangled photons. States of maximal entanglement, entanglement entropy, quantum teleportation and quantum cryptography. (mainly from Trahanas, Chapters 14-15, 2 weeks)
Bibliography
1. «Κβαντομηχανική ΙΙ» - Στ. Τραχανάς, Πανεπιστημιακές Εκδόσεις Κρήτης
2. «Lectures on Quantum Mechanics» - Steven Weinberg, Cambridge University Press
2. «Lectures on Quantum Mechanics» - Steven Weinberg, Cambridge University Press
