On the electrostatic potential due to a slab shaped and a semi-infinite NaCl-type lattice

Consider N layers of a NaCl-type ionic lattice such that in every layer one has an infinite square lattice of positive and negative unit point charges. We present formulae in which the electrostatic potential in an arbitrary field point is expressed as a sum of two rapidly converging lattice sums. For N→∞ we obtain formulae applicable for a semi-infinite lattice

On the electrostatic potential due to a slab shaped and a semi-infinite NaCl-type lattice

Consider N layers of a NaCl-type ionic lattice such that in every layer one has an infinite square lattice of positive and negative unit point charges. We present formulae in which the electrostatic potential in an arbitrary field point is expressed as a sum of two rapidly converging lattice sums. For N→∞ we obtain formulae applicable for a semi-infinite lattice

Some remarks on the theory of the dielectric constant of non-polar dense gases

It is pointed out that the usual simple theory of the dielectric constant in isotropic nonpolar media, based on a model with constant polarizability and with dipolar interaction between atoms, is consistent only if the atoms are assumed to have a hard core, so that they cannot approach each other too closely. The expansion of the dielectric constant in powers of the polarizability α is obtained in a simple way. The two-particle contribution to the deviation S (α, ρ, T) from the law of Clausius-Mossotti is summed to all orders in α and in particular the term of S (α, ρ, T) linear in the denity ρ is discussed

On the many-body Van der Waals binding energy of a dense fluid

We consider a dense system of neutral atoms. When the atoms are represented by isotropic oscillators (Drude-Lorentz model) interacting with nonretarded dipole-dipole forces, the binding energy of the system is given exactly by a well-known expression which is written as a sum of two-bond, three-bond, etc., Van der Waals interactions. For a Bravais lattice this expression for the binding energy can be computed numerically to arbitrary accuracy. This has been done for the f.c.c. lattices of the noble-gas solids by Lucas. For a fluid an exact evaluation would require the knowledge of higher-order molecular distribution functions. Various approximations are discussed for this case, the simplest of which is the so-called long-wavelength approximation due to Doniach. When this approximation is checked by comparison with the exact result for a lattice, it turns out that the two-bond contribution leads to a value which is more than twice too large. Some more refined approximations are considered which treat the two-bond contribution exactly. It is pointed out that the model is consistent only if the distance of closest approach between the atoms is not too small

The wigner distribution function for systems of bosons or fermions

An expression for the Wigner distribution function valid for systems of bosons or fermions is obtained by making use of correspondence relations between classical quantities and quantum mechanical operators first given by Groenewold. A general and straightforward derivation of the equation of motion for the Wigner distribution function is presented. The equation governing the temperature dependence of the Wigner distribution function in the case of a canonical ensemble can be derived in a completely analogous way

On the statistical mechanics of matter in an electromagnetic field. I. Derivation of the maxwell equations from electron theory

Maxwell's macroscopic field equations are derived from the fundamental microscopic equations of electron theory in a new way. Instead of the usual space-time averaging procedure a statistical ensemble averaging method is applied, which is perhaps more satisfactory both from a physical and from a mathematical point of view. The treatment is valid for multicomponent systems, in which every component may move in an arbitrary way, so that e.g. diffusion phenomena are included. Furthermore it would seem that the method given here is also suitable for the discussion of other problems connected with the behaviour of matter in an electromagnetic field

Microscopic derivation of macroscopic Van der Waals forces

For a general system of isotropic harmonic oscillators with non-retarded dipole interaction a formula for the interatomic forces is derived. It is used to give an atomistic derivation of macroscopic Van der Waals forces in terms of the dielectric constant