An Approximate Quantum Theory of the Antiferromagnetic Ground State

A careful treatment of the zero-point energy of the spin-waves in the Kramers-Heller semiclassical theory of ferromagnetics leads to surprisingly exact results for the properties of the ground state, as shown by Klein and Smith. An analogous treatment of the antiferromagnetic ground state, whose properties were unknown, is here carried out and justified. The results are expected to be valid to order $\frac{1}{S}$ or better, where $S$ is the spin quantum number of the separate atoms.