Electric dipole in a magnetic field: Bound states without classical turning points

We show that both rigid and nonrigid dipoles can be trapped by an uniform external magnetic field in classical mechanics. The trapped states of the dipole present a nontrivial example of classical bound states embedded in a continuum (BSEC) that can be treated as analogues of quantum BSECs. For example, the classical motion of the dipole is confined to a finite region in space although there are no classical turning points. We also examine the quantum motion of the dipole in a magnetic field and show that for the most natural choices of the parameters, no quantum BSEC solutions exist. The possibilities of experimental investigations of BSECs are discussed.