Semiclassical eigenvalues for non-separable bound systems from classical trajectories: the higher energy levels

Abstract

Previously proposed quantum conditions are used to calculate the higher eigenvalues of a simple two-dimensional (2D) potential from classical trajectories. A new modification to our earlier work is introduced to deal with problems arising from the complicated behaviour of the caustics in certain cases. Results are in excellent agreement with quantum-mechanical calculations. Our methods are shown to be competitive with quantum calculations in their ease of application for these upper levels. However, it is not possible to calculate certain semiclassical eigenvalues near the escape energy because corresponding trajectories are ergodic.