Theory of a Polaron with an Anisotropic Mass in External Fields

The intermediate coupling theory is applied to the problem of a polaron with an anisotropic mass. The energy levels of a polaron bound in a Coulomb potential are discussed. Hydrogenic wave functions are used as variational wave functions, and it is shown that each energy level depends not only on the principal quantum number but also on the azimuthal and magnetic quantum numbers owing to the anisotropy of the mass. The electric polarizability of a bound polaron is also calculated, and the effect of a weak magnetic field is discussed both in the absence and the presence of a Coulomb potential.