Classical counterpart of wave functions for two-dimensional open waveguides

We propose a purely classical counterpart of wave functions in coordinate space for two-dimensional waveguides. Comparison between the wave functions and their classical counterparts allows us to associate the classical dynamical origin of certain features that appear in the quantum description of the system. We show that the classical wave functions may be used as a tool for predicting the global structure of their quantum counterparts even in the quantum regime. We also discuss the limits of our classical approach.