Study level
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 begins with the study of situations where the solution is analytical, followed by situations where the solution is semi-analytical, before tackling the finite-difference method DF. Different DF schemes are proposed, each time with an evaluation of convergence as a function of various key parameters (domain truncation, number of samples, etc.). Finally, examples of concrete physical applications are studied.
Objectives
Mastery of the finite-difference method for simulating quantum structures (complex quantum wells, etc.).
Necessary prerequisites
Basic quantum mechanics: quantum wells
Recommended prerequisites:
Common programming languages matlab/octave
Knowledge control
Final examination
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 begins with the study of situations where the solution is analytical, followed by situations where the solution is semi-analytical, before tackling the finite-difference method DF. Different DF schemes are proposed, each time with an evaluation of convergence as a function of various key parameters (domain truncation, number of samples, etc.). Finally, examples of concrete physical applications are studied.