Confined many-electron systems

The problem of the influence of spatial confinement on the physical and chemical properties of many quantum mechanical systems is discussed. It covers low-dimensional electron gas or impurity atoms in artificial mesoscopic scale semiconductor structures as well as atoms and molecules trapped in microscopic cavities like molecular zeolite sieves. Particular emphasis is put on the methods for calculating the influence of a confinement on the electronic structure of the confined objects. More attention is paid to the surface Green function matching (SGFM) formalism and to the concept of a Green function satisfying periodic boundary conditions, Applications to an electron gas confined in different types of quantum wells are briefly discussed. Other methods, in particular those used for description of 1D and 0D systems, are also presented. Exactly solvable models of spatially confined atoms are reviewed. Approximate methods for describing the energy structure of impurity atoms and excitons in low-dimensional systems sire also presented. For the case of atoms and molecules trapped in zeolite-like cavities the methods, which reduce to simple modifications of the commonly used basis set quantum chemical calculations are discussed with more details.