Barker, L.2016-02-082016-02-0820010022-2488http://hdl.handle.net/11693/24806Convergence of a "discrete" operator to a "continuum" operator is defined. As examples, the circular rotor, the one-dimensional box, the harmonic oscillator, and the fractional Fourier transform are realized as limits of finite-dimensional quantum systems. Limits, thus defined, preserve algebraic structure. The results prepare for a sequel in which some affine canonical transforms will be "discretized." © 2001 American Institute of Physics.EnglishArticle10.1063/1.13985821089-7658