Waving arms around to teach quantum mechanics

Abstract

Kinesthetic (or embodied) representations help students build intuition and deep understanding of concepts. This paper presents a series of kinesthetic activities for a spins-first undergraduate quantum mechanics course that supports students in reasoning and developing intuition about the complex-valued vectors of spin states. The arms representation, used in these activities, was developed as a tangible representation of complex numbers: Students act as an Argand diagram, using their left arm to represent numbers in the complex plane. The arms representation is versatile and can be expanded to depict complex-valued vectors with groups of students. This expansion enables groups of students to represent quantum mechanical state vectors with their arms. We have developed activities using the arms representation that parallel the progression of a spins-first approach by starting with complex numbers, then representing two- and three-state systems, considering time-dependence, and, eventually, extending to approximate wavefunctions. Each activity illustrates the complex nature of quantum states and provides a tangible manipulative from which students can build intuition about quantum phenomena.