Level of education
Master's degree
ECTS
3 credits
Training structure
Faculty of Science
Hours per week
21h
Description
This course is designed to provide students with skills in the field of numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course begins by studying situations where the solution is analytical, then situations where the solution is semi-analytical, before moving on to the finite difference (FD) method. Various FD schemes are proposed, each with an evaluation of convergence based on different 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.).
Mandatory prerequisites
Basic quantum mechanics: quantum wells
Recommended prerequisites:
Common programming languages matlab/octave
Knowledge assessment
Final exam
Syllabus
This course is designed to provide students with skills in the field of numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course begins by studying situations where the solution is analytical, then situations where the solution is semi-analytical, before moving on to the finite difference (FD) method. Various FD schemes are proposed, each with an evaluation of convergence based on different key parameters (domain truncation, number of samples, etc.). Finally, examples of concrete physical applications are studied.