Level of study
BAC +5
ECTS
3 credits
Component
Faculty of Science
Hourly volume
21h
Description
This course is designed to give students skills in the numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course starts with the study of situations where the solution is analytical, then situations where the solution is semi-analytical before attacking on the finite difference method FD. Different FD schemes are proposed with, each time, an evaluation of the convergence according to different key parameters (truncation of the domain, number of samples...). Finally, examples of concrete physical applications are studied.
Objectives
Mastery of the finite difference method for the simulation of quantum structures (complex quantum wells...).
Necessary pre-requisites
Basic quantum mechanics: quantum wells
Recommended Prerequisites:
Common programming languages matlab/octave
Knowledge control
Final exam
Syllabus
This course is designed to give students skills in the numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course starts with the study of situations where the solution is analytical, then situations where the solution is semi-analytical before attacking on the finite difference method FD. Different FD schemes are proposed with, each time, an evaluation of the convergence according to different key parameters (truncation of the domain, number of samples...). Finally, examples of concrete physical applications are studied.