Landau levels for charged particles with anisotropic mass

The problem of the two-dimensional motion of a charged particle with constant mass in the presence of a uniform constant perpendicular magnetic field features in several undergraduate and graduate quantum physics textbooks. This problem is very important to studies of two-dimensional materials that manifest quantum Hall behavior, as evidenced by several major discoveries over the last few years. Many real experimental samples are more complicated due to the anisotropic mass of the electrons. In this work, we provide the exact solution to this problem by means of a clever scaling of coordinates. Calculations are done for a symmetric gauge of the magnetic field. This study allows a broad audience of students and teachers to understand the mathematical techniques that lead to the solution of this quantum problem.