A Review of Quantum Confinement

摘要

A succinct history of the Confined Atom problem is presented. The hydrogen atom confined to the centre of an impenetrable sphere counts amongst the exactly soluble problems of physics, alongside much more noted exact solutions such as Black Body Radiation and the free Hydrogen atom in absence of any radiation field. It shares with them the disadvantage of being an idealisation, while at the same time encapsulating in a simple way particular aspects of physical reality. The problem was first formulated by Sommerfeld and Welker [1] - henceforth cited as SW - in connection with the behaviour of atoms at very high pressures, and the solution was published on the occasion of Pauli's 60~(th) birthday celebration. At the time, it seemed that there was not much other connection with physical reality beyond a few simple aspects connected to the properties of atoms in solids, for which more appropriate models were soon developed. Thus, confined atoms attracted little attention until the advent of the metallofullerene, which provided the first example of a confined atom with properties quite closely related to those originally considered by SW. Since then, the problem has received much more attention, and many more new features of quantum confinement, quantum compression, the quantum Faraday cage, electronic reorganisation, cavity resonances, etc have been described, which are relevant to real systems. Also, a number of other situations have been uncovered experimentally to which quantum confinement is relevant. Thus, studies of the confined atom are now more numerous, and have been extended both in terms of the models used and the systems to which they can be applied. Connections to thermodynamics are explored through the properties of a confined two-level atom adapted from Einstein's celebrated model, and issues of dynamical screening of electromagnetic radiation by the confining shell are discussed in connection with the Faraday cage produced by a confining conducting shell. The conclusions are shown to be relevant to a proposed 'quantum computer'. The description of the actual geometry of C_(60) as opposed to a purely spherical approximation, leads to some qualification of the computed results.