  We suggest a mathematical potential well with spherical symmetry and apply to
the 1d Schr\"odinger equation. We use some well-known techniques as Stationary
Perturbation Theory and WKB to gain insight into the solutions and compare them
to each other. Finally, we solve the 1d Schr\"odinger equation using a
numerical approach with the so-called Numerov technique for comparison. It can
be a good exercise for undergrad students to grasp the above-cited techniques
in a quantum mechanics course.
