Localization and other common features of degenerate perturbations

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Abstract
Diverse problems lead to groups of states with wave functions localized into different regions of space. This result is shown to be characteristic of a large number of problems in physics (atomic and nuclear examples are given) where states of highly degenerate manifolds are mixed by an interaction, which may be one or two particle in nature. Common analytical structures are derived and their origin traced. Random distributions and statistical arguments have often been used for the form of the localization which we derive, however, as a consequence of specific structures in the interaction Hamiltonians.