Quantum bound states embedded in a continuum and their classical analogs

We show that both a rigid and a nonrigid dipole can be trapped by an external uniform magnetic field in classical mechanics. The trapped states of a dipole present a nontrivial example of classical bound states embedded in a continuum (BSEC) that can be treated as analogs of quantum BSECs. For example, the classical motion of a dipole is confined to a finite region in space, though there are no classical turning points. We also examine the quantum motion of a dipole in a magnetic field and show that, for the most natural choices of the parameters (the rigid rotating dipole or the one bound by oscillator potential, uniform time-independent magnetic field, etc.), there are no quantum BSEC solutions.