Physical Review A
American Physical Society
The behavior of an atomic electron in a static magnetic field strong enough to correspond to the transition regime is examined. The field strength is characterized by the parameter L^, the effective component of angular momentum. A Floquet-Mathieu analysis shows that the bifurcation of classical trajectories into elliptical and helical families is related to the 2:1 resonance which occurs at L^=L^T. Quantum mechanics gives an avoided crossing at L^T; we examine the nature of the wave functions as L^ passes through the resonance. Semiclassical calculations accurately reproduce the quantum eigenvalues and produce trajectories which underlie the quantum wave functions. The avoided crossing is expressed in semiclassical terms as a switch between elliptical and helical families. The bifurcation of the classical motion means that, at the primitive semiclassical level, some states may be missed and others may be generated in both elliptical and helical representations.
Delos, John B.; Knudson, Stephen; Sikora, Shena; Waterland, Robert Leonard; and Whitworth, S., Atomic Electrons in Strong Magnetic Fields: Transition from Elliptical to Helical Behavior. (1988). Physical Review A, 37(12), 4582-4598.