A WKB approach to quantum Hall states

In the present work, we focus on the study of bi-dimensional evolution of the complex scalar field, within the phase-integral approach. We start by writing down the quantum eigenstates and the Landau-type energy levels, which are exhibiting a general dependence on the external static fields. Fixing the width of the sample, we employ the WKB calculus for bounded harmonic oscillators for deriving the energy correction, particle momentum and electromagnetic current, in terms of an energy-related excess fractal dimension.