The Superformula and model quantum systems as tools for learning

Our understanding of quantum phenomena often begins with simple particle-in-a-box style problems, the solutions of which introduce the student to foundational quantum concepts such as degeneracy and quantization. Simple model geometries of confinement afford analytic solutions, which are readily derivable, easily manipulable, and provide a unique sandbox of exploration accessible at the undergraduate level. In the current work, these model problems are explored in a variety of ways. Firstly, through a historical lens - orienting them to the birth and development of quantum physics. Then, via an organizing syntax. This framework allows the interested student to orient the diverse multidisciplinary literature that has evolved around these problems. Finally, through consideration of the shape element of the syntax, the superformula a simple extension of the equation describing a circle is introduced and discussed.