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Landscape of uncertainty in Hilbert space for one-particle states

Weigert, S. (orcid.org/0000-0002-6647-3252) (1996) Landscape of uncertainty in Hilbert space for one-particle states. Physical Review A. pp. 2084-2088. ISSN 1094-1622

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The functional of uncertainty J[¿] assigns to each state ¿¿> the product of the variances of the momentum and position operators. Its first and second variations are investigated. Each stationary point is located on one of a countable set of three-dimensional manifolds in Hilbert space. For a harmonic oscillator with given mass and frequency the extremals are identified as displaced squeezed energy eigenstates. The neighborhood of the stationary states is found to have the structure of a saddle, thus completing the picture of the landscape of uncertainty in Hilbert space. This result follows from the diagonalization of the second variation of the uncertainty functional, which is not straightforward since J[¿] depends nonlinearly on the state ¿¿>.

Item Type: Article
Copyright, Publisher and Additional Information: © 1996 The American Physical Society. Reproduced in accordance with the publisher's self-archiving policy.
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: Repository Officer
Date Deposited: 23 Jun 2006
Last Modified: 17 May 2016 07:20
Published Version: http://dx.doi.org/10.1103/PhysRevA.53.2084
Status: Published
Refereed: Yes
URI: http://eprints.whiterose.ac.uk/id/eprint/1365

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