Numerical calculation of the allowed wavefunctions in a one-dimensional infinite potential well
Initial Publication Date: October 14, 2024
Summary
Numerical calculation of the allowed wavefunctions in a one-dimensional infinite potential well
Learning Goals
At the end of this lab you should:
- Be able to explain why it is often necessary to use a computer in order to find numerical solutions to a differential equation.
- Be able to describe what it means to discretize a differential equation and why it is necessary to do so in order to solve the equation using a computer.
- Have practiced plotting, array manipulation, and data analysis using MATLAB.
Context for Use
This is done during a 3.5 hour laboratory for a sophomore-level Modern Physics course for Physics and Electrical Engineering majors.
Description and Teaching Materials
Quantum_Dot_Lab_Livescript.mlx (MATLAB Live Script 59kB Oct4 24)
Teaching Notes and Tips
Students often struggle with using the correct units throughout the lab.
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Assessment
Students submit the lab as a pdf. Instructors grade based on the plots and answers to the final reflection question.
References and Resources
A.F.J. Levi, Applied Quantum Mechanics, 2nd ed. Cambridge University Press, United Kingdom (2006), and W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 5th ed. Thomson Brooks/Cole, United States of America (2004).