This exercise is one of our favorites, and we have adapted it to advanced Bachelor's and graduate courses as well. Students are asked to explore the differences in the energy spectrum that arise as one changes the potential from the infinite square well to a harmonic well and even beyond.

Key words and phrases: quantum harmonic oscillator, infinite square well, energy spectra, eigenvalues, anharmonic oscillator

The exercise PDF can be found here.

A zip folder containing the relevant flow file (which is the same as the previous introductory exercise and the final exercise on the infinite square well) can be found here.