Self-consistent field equations for the dipole moments of point polarizable atoms in slabs of cubic lattices with a uniform applied electric field are constructed. Results of Toeplitz operator theory are used to characterize the ranges of atomic polarizability for which there are unique...

The ground-state energy of a low-density hard-disk Fermi gas is analysed with a variational calculation and with a perturbation-theory summation. The results of the analyses for the first two terms in the energy, the Fermi energy and the analogue of the Lenz interaction energy, agree with each...