Anderson's (1958) theory of localized electron states in an irregular solid is discussed critically. The statistical and analytical properties of the Green function, when states are localized, are analyzed and it is pointed out that these are not incompatible with Lloyd's (1969) exact results. Anderson's argument is repeated in outline, but it has been found possible to make a major simplification in the statistical analysis. Attention is drawn to two doubtful points in the argument and it is suggested that delocalization occurs less easily than Anderson supposed. The argument is applied to a model of a dilute binary alloy. It is proved for a model of the binary alloy that the energy levels do not extend outside the energy bands of the pure metals.
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