XX. Properties of slow electrons in polar materials

Summary Using a variational method we have investigated the properties of the lowest energy levels in a range ħω above the ground level of the system consisting of an electron and a continuous dielectric medium. The latter is supposed to have a single vibrational frequency ω/2π for long longitudinal polarization waves. The interaction between the electron and the medium then depends on three parameters, the static dielectric constante, ∈ the optical refractive index , and ω. The replacement of a crystalline lattice by a continuum is a good approximation if the length b= (ħ/2mω)1/2 is large compared with the lattice distance, a condition which is usually fulfilled.