The Superformula and Model Quantum Systems as Tools for Learning

Abstract

The Superformula is a generalization of the series of closed curves, called Superellipses, and represents a generalization of the circle. The Superformula describes a wide range of abstract and naturally occurring shapes and has an accessible functional form containing a small number of parameters. In the current work, the Superformula is used as a flexible confining geometry defining a novel class of confined model quantum systems, the “particle-in-a-Superformula”. Following its introduction, we describe the use of the “particle-in-a-Superformula” model in an undergraduate context. A guided exploration of these systems by a small group (N = 9) of multidisciplinary undergraduate students over four 90 min sessions is shared. The construction of, and the collected responses to, a short survey vehicle describing their thoughts and experience is detailed. In general, the students were positive about their use of this flexible construct as an aid to their facility with, and learning of, quantum phenomena.