Physical insights from the "skew" infinite square well

The skew infinite square well is characterized by a linear potential between two infinitely high potential barriers. Curiously, this particular one-dimensional potential problem is not treated in quantum mechanics courses or textbooks even though it has an analytical solution. We aim to show students how concepts such as symmetries of wavefunctions can be used to determine the approximate ground state energy of the skew well using the wavefunctions of the classic infinite square well. Undergraduate and graduate students will benefit from seeing concepts such as matrix diagonalization and perturbation theory applied to a cute problem that contains physical insights that are unintuitive in the analytical solution.