Conceptual inconsistencies in finite-dimensional quantum and classical mechanics

Denys I. Bondar, Renan Cabrera, Herschel A. Rabitz

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Utilizing operational dynamic modeling, 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.

Original languageEnglish (US)
Article number012116
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume88
Issue number1
DOIs
StatePublished - Jul 16 2013

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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