Comparison of quantal, classical, and semiclassical behavior at an isolated avoided crossing

Abstract

The quantal and classical/semiclassical behavior at an isloated avoided crossing are compared. While the quantum mechanical eigenvalue perturbation parameter plots exhibit the avoided crossing, the corresponding primitive semiclassical eigenvalue plots pass through the intersection. Otherwise, the eigenvalues agree well with the quantum mechanical values. The semiclassical splitting at the intersection is calculated from an appropriate Fourier transform. In the quasiperiodic regime, a quantum state near an avoided crossing is seen to exhibit typically more delocalization than the classical state. However, trajectories near the "separatrix" display a quasiperiodic "transition" between two zeroth order classical states.