|Title||Using Arms to Represent Complex-Valued Vectors in Quantum Mechanics|
|Year of Publication||2021|
|Authors||Hahn, Kelby T., and Gire Elizabeth|
|Keywords||ARMS, Quantum Mechanics|
The Paradigms @ OSU team developed a representation for complex numbers where students use their arms to embody an Argand diagram. By grouping students, the Arms Representation can be expanded to represent complex-valued vectors. The Arms Activity Sequence utilizes this expanded form to enable groups of students to represent quantum mechanical state vectors. In this talk we will present the Arms Representation and the Arms Activity Sequence. We will discuss how the sequence supports a spins-first approach by starting with complex numbers, advancing through two- and three-state systems, considering time-dependence, and eventually extending to approximate wavefunctions. The Arms Representation exemplifies the complex nature and geometric definition of a quantum state. We will highlight the development of these and other mathematics and physics concepts in the sequence and provide pedagogical tips for its implementation.