4. Homework¶

Use the computational techniques you have studied this week to answer the following question and submit your answers as a single .py file.

1. Find the energy levels for the quantum harmonic osicllator using the matrix ODE methods, here \(V = -\frac{1}{2}m \omega^2\,x^2\).

2. Plot the first three (eigen) wave functions on a graph

3. Show that (to a threshold accuracy) the solutions are orthogonal and find this threshold.

4.1. References¶

[1] James R. Chelikowsky, Introductory Quantum Mechanics with MATLAB®: For Atoms, Molecules, Clusters, and Nanocrystals. Wiley Press, 2019.

[2] David S. Sholl; Janice A. Steckel, Density Functional Theory. Wiley Press, 2009.