Classical and quantum binding of a particle with arbitrary spin in the magnetic field of a current-carrying wire: A simple guide for atoms

A neutral atom with a magnetic moment can be bound to, and guided along, a current-carrying wire. The atom is attracted to regions of high field strength (high-field seeking stare) and repelled from the wire by the centrifugal barrier. In the classical regime the atoms move in Kepler-like orbits. In the quantum regime, the system resembles a two-dimensional hydrogen atom in Rydberg-like states. The wire replaces the nucleus and the atom plays the role of the electron. We give a quantum mechanical and a classical description of the system. We rigorously prove the existence of infinitely many bound states for zero or finite wire cross section and any spin (F) of the atom. The bound-stare energies closely follow a Coulomb-like behaviour with an effective angular momentum, l(eff).