Anomalous states from a classical Hamiltonian: Electric dipole in a magnetic field

In the present study, we obtain the equations of motion for an electric dipole in the presence of a uniform magnetic field, by the Lagrangian formulation. Solutions can be represented in terms of Jacobi functions. Thus, we identify two constants of motion, the energy ℰ and a pseudomomentum C→ . We obtain a relation between the constants that suggests the existence of a type of bound states without turning points, which are called trapped states. The present results are complementary to other ones previously reported by Troncoso and Curilef [2006 Eur. J. Phys. 27 1315].