Spin Waves in an Interacting Electron Gas

Some previous results of the author in collaboration with H. Brooks are improved and corrected concerning the coefficient of $q^2$ in the spin-wave dispersion law in an electron gas interacting according to a Yukawa potential. A variational method of solution for the integral equation occurring in this theory is given which, besides giving the spin-wave energy correctly, also gives the spin-density-wave instability when extended suitably. Having uncovered the instability of the paramagnetic state, an alternative derivation of the new state is given by a Green's-function method. In an Appendix, a theory of spin-density waves in a Bloch electron system is outlined. The variational method given here seems to be of quite general use in solving similar problems in other contexts.