Παρουσίαση/Προβολή

(QE5) -  Emmanuel Paspalakis

Περιγραφή Μαθήματος

This is an elective course in the MSc in Quantum Computing and Quantum Technologies

The course for the winter semester 2025-26 is taught every Thursday from 18:00-20:00 CET.

This course presents the basics of quantum mechanics aiming at the understanding of the critical role of quantum mechanics in determining the behavior of practical devices. The intent of this course is to create the beginning of a quantum toolbox for people interested in understanding and applying quantum mechanics to new ideas in technology. The course syllabus includes:

Basic features: Time-dependent and time-independent Schrödinger equation, operators, expectation values, probability density and probability current density, eigenvalues and eigenstates, superposition principle, uncertainty principle. Dirac notation.

Solutions of the time-independent Schrödinger equation in simple and more complex one-dimensional potentials: Free-particle, symmetric quantum wells, combination of infinite and finite-barrier potential wells. Delta function potential, combination of delta function potentials and heterostructures or quantum wells, triangular potential. 

Scattering in one dimension: Transmission and reflection coefficients, tunneling in simple and complex barriers. The propagation matrix method. Resonant tunneling, WKB approximation for tunneling.

Periodic potential: Solution of the time-independent Schrödinger equation for a periodic potential.

Harmonic oscillator: Algebraic method of the harmonic oscillator, creation and annihilation operators. Stark effect in the harmonic oscillator, quantization of the LC circuit, free electron in a magnetic field - Landau states.

Electron in two- and three-dimensional separable potentials and central potentials: Separable rectangular, square and cubic potentials, two and three-dimensional harmonic oscillators. Quantum wells, wires, and dots. Central potentials, angular momentum, spherical harmonics and radial equation. Application to spherical potentials and solution for hydrogen-like systems.

Spin and its properties. Addition of angular momenta.

Approximation methods for the solution of the Schrödinger equation: Time-independent non-degenerate perturbation theory and applications. Time-independent degenerate perturbation theory and applications Variational method and WKB approximation for stationary states and their applications. The sudden approximation and applications.

Identical particles: Pauli exclusion principle, the symmetry of the wavefunctions and applications.

Ημερομηνία δημιουργίας

Παρασκευή 6 Οκτωβρίου 2023