Asymptotic Techniques For Atomic Waveguide Calculations

Asymptotic expansions describing the behavior of the radial wavefunctions of a magnetic atomic waveguide are developed. In this system, some components of the spinor wavefunctions do not die off exponentially and are therefore significant at large distances. This is related to the quasibound nature of the system. A good representation of the nondecaying components of the eigenstates at large distances from the guide center is required so that the calculated eigenstates can be used reliably in further numerical calculations. The asymptotic expansions presented here provide this representation and are readily related to the power series solutions developed in ARL-TR-5335. By connecting those power series solutions to the asymptotic expansions developed here, an efficient representation of the exact radial wavefunctions can be obtained. These wavefunctions are needed for detailed studies of important properties of magnetic guides such as sensitivity to noise driven spin flips, importance of quantum Majorana transitions, energy level dependence on magnetic field, the effects of guiding field imperfections as well as the onset and departure of adiabatic behavior.