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Conceptual inconsistencies in finite-dimensional quantum and classical mechanics

Author(s): Bondar, Denys I.; Cabrera, Renan; Rabitz, Herschel A.

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Abstract: Utilizing operational dynamic modeling [D. I. Bondar et al., Phys. Rev. Lett. 109, 190403 (2012)], we demonstrate that any finite-dimensional representation of quantum and classical dynamics violates the Ehrenfest theorems. Other peculiarities are also revealed, including the nonexistence of the free particle and ambiguity in defining potential forces. Non-Hermitian mechanics is shown to have the same problems. This work compromises a popular belief that finite-dimensional mechanics is a straightforward discretization of the corresponding infinite-dimensional formulation.
Publication Date: 16-Jul-2013
Citation: Bondar, Denys I., Cabrera, Renan, Rabitz, Herschel A. (2013). Conceptual inconsistencies in finite-dimensional quantum and classical mechanics. PHYSICAL REVIEW A, 88 (10.1103/PhysRevA.88.012116
DOI: doi:10.1103/PhysRevA.88.012116
ISSN: 1050-2947
Pages: 012116-1 - 012116-5
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW A
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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