Continuum quantum systems as limits of discrete quantum systems. III. Operators
Journal of Mathematical Physics
A I P Publishing LLC
4653 - 4668
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Convergence 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.