Inelastic neutron scattering measurements by Okazaki, Tuberfield, and Stevenson (1964) of the antiferromagnetic spin wave energy, spectrum in manganese fluoride crystal at low temperatures, agree with the results predicted by a dispersion relation introduced without proof in their paper. In this thesis the question is considered in detail to what extent this dispersion relation is justified. The interaction between the manganese ions is described by the Heisenberg exchange Hamiltonian. Following Holstein and Primakoff's formalism the spin deviation operators are introduced and the part of the Hamiltonian ℋ[superscript B] containing all the terms up to those bilinear in the spin deviation operators is diagonalised by means of the Anderson transformation. A correction is next obtained by retaining the diagonal part of those terms which are quadrilinear in the spin deviation operators. Under certain conditions it is shown that ℋ[superscript B] together with the correction term give rise to, a dispersion relation which is identical with that used by Okazaki et al. (1964). Finally the validity of the approximations is also discussed. / Science, Faculty of / Physics and Astronomy, Department of / Graduate