Abstract
This chapter treats a number of problems concerning systems that either have a highly restricted number of degrees of freedom, or are described by a finite-dimensional Hilbert space. Problems of the first type are familiar from classical mechanics, but those of the second type have no classical counterpart whatever. All the systems of classical physics, whether they be particles or fields, have degrees of freedom with continuous values and require infinite-dimensional Hilbert spaces for their quantum mechanical description. For that reason, a full-fledged treatment of any phenomenon ultimately involves such a space. Nevertheless, finite-dimensional state spaces are of great importance, both in the description of actual experiments and in discussions of the foundations of quantum mechanics.
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