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Continuum Quantum Systems as Limits of Discrete Quantum Systems, I: State Vectors

✍ Scribed by Laurence Barker

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
136 KB
Volume
186
Category
Article
ISSN
0022-1236

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✦ Synopsis

Dynamical systems on ''continuum'' Hilbert spaces may be realized as limits of dynamical systems on ''discrete'' (possibly finite-dimensional) Hilbert spaces. In this first of four papers on the topic, the ''continuum'' and ''discrete'' spaces are interfaced to one another algebraically, convergence of vectors is defined in such a way as to preserve inner products, and a necessary and sufficient coordinate-wise criterion for convergence is proved.

πŸ“œ SIMILAR VOLUMES

The Continuum Limit of Quantum Spin Syst
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✍ A.M. Fearnhead; K.C. Hannabuss πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 211 KB

An extension of the quantum mechanical central limit theorem provides a linear continuum model of the quantum fluctuations near a stable pumped state of a discrete atomic model such as the Dicke Hepp Lieb maser model. This procedure can be reversed to select an appropriate atomic model whose limit g