Confined many-electron systems 

                 W. Jaskolski

   Instytut Fizyki, Uniwersytet Mikolaja Kopernika, 
        Grudziadzka 5, 87-100 Torun, Poland

                    Abstract 

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 are 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.