Continuum quantum systems as limits of discrete quantum systems. III. Operators
- 1 October 2001
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 42 (10) , 4653-4668
- https://doi.org/10.1063/1.1398582
Abstract
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.”Keywords
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