878 resultados para positivity preserving


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Includes bibliographical references (p. 48-50).

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Shipping list no.: 97-0056-P.

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Pt. 5 issued by the subcommittee under its later name: Subcommittee on Reorganization, Research, and International Organizations.

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Includes bibliographical references (p. 313-314) and index.

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A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Lionville densities, leading to what may be termed Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Lionville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.