Quantum ring in the eyes of geometric (Clifford) algebra

Abstract

The quantum ring with spin–orbit interaction included is analyzed in a nonstandard way using Clifford or geometric algebra (GA). The solution of the Schrödinger–Pauli equation is presented in terms of rotors having clear classical mechanics interpretation, i.e., in GA the rotors act in 3D Euclidean space rather than as operators in an abstract Hilbert space. This classical-like property of spin control in GA provides a more transparent approach in designing and understanding spintronic devices. The aim of the paper is to attract readers attention to new possibilities in spin physics and to demonstrate how the quantum ring problem can be solved by GA methods.