Cyclotron motion of a charged particle with anisotropic mass

Abstract

The cyclotron motion of a charged particle subject to a uniform magnetic field is thoroughly described in many classical physics textbooks. Although the assumption of a particle with isotropic mass is taken for granted in classical physics, a key concept in condensed matter physics is that of particles with an effective anisotropic mass, such as electrons in the context of band structure studies of solids. Since some exposure to the concept of anisotropic mass is important within the framework of classical physics, here we consider the cyclotron motion of a charged particle with anisotropic mass in the presence of a uniform magnetic field. The exact solution of this problem exposes a broad audience of readers to concepts in condensed matter physics that are rarely mentioned within the framework of classical physics. Key ideas on the topic are illustrated in a pedagogical way by considering specific examples that show how an anisotropic mass modifies the cyclotron motion of a charged particle.