The origin of the Shubnikov-de Haas effect, the strain theory developed by Bir and Pikus, and a simple, classical beating-effects model are discussed. The equipment and the experimental techniques used in recording the Shubnikov-de Haas oscillations of n-type indium antimonite are described. The analysis of the experimental data showed that the angular anisotropy of the period of SdH oscillations at zero stress was unmeasurable for low concentration samples as discussed by other workers. Thus the Fermi surfaces of InSb are nearly spherical at low concentration. It was also shown that the Fermi surface of a high concentration sample of InAs is also nearly spherical. The advantages of using the magnetic field modulation and phase sensitive detection techniques in determining the beats are given. The simple, classical beating-effects model is able to explain the experimental beating effect data in InSb. The computer programs used to obtain the theoretical values of the beat nodal position, SdH frequencies, average frequency, the Fermi surface contours, and the energy eigenvalues are given.

The finite lifetime of the bound roton pair is included in the theoretical light scattering cross section to explain the shape of the peak in the observed Raman light scattering cross section in He II. A model Hamiltonian is used to describe interactions between quasiparticles for the helium system. The equation of motion for the bound roton pair state, which is taken to be a collective mode of quasiparticle pairs, is solved. The cross section for light scattering is then derived using Fermi's Golden Rule with the bound roton pair as the final state. Since the bound roton pair can decay into two free phonons, a phenomenological width r is included in the cross section. The peak position and shape of the observed cross section are both fitted using a binding energy of εB = 0.37 K for the bound roton pair.

An expression for the dielectric susceptibility tensor of a cubic ionic crystal has been derived using the classical Liouville operator. The effect of cubic anharmonic forces is included as a perturbation on the harmonic crystal solution, and a series expansion for the dielectric susceptibility is developed. The most important terms in the series are identified and summed, yielding an expression for the complex susceptibility with an anharmonic contribution which is linearly dependent on temperature. A numerical example shows that both the real and imaginary parts of the susceptibility are continuous, finite functions of frequency.