Influence of confinement on the properties of quantum systems

A quantum system (an atom, a molecule, a cluster) confined within a cavity behaves differently from a free system. In this report some general relations between the form of the confining potential and the properties of the confined system are presented and discussed. Several examples are given to illustrate the models. In particular, a number of exactly or quasi-exactly solvable models describing free electrons bound in an external confining potential are discussed and their spectra are analyzed. The results, apart of their academic interest, are important in spectroscopy of plasma, give new insight into properties of quantum dots, explain behavior of atoms and molecules under high pressure. It appears that the understanding of the relations between the form of the confining potential and the structure of the confined molecule may be essential for engineering chemical reactions and for creating conditions under which the cold muonic fusion might be possible.