2011/12/31 by Denys I. Bondar, Renan Cabrera, Herschel A. Rabitz
Physics and Astronomy · Mathematics · #quant-ph #math-ph #math.MP
paper · pdf · doi:10.1103/physreva.88.012116
published as Phys. Rev. A 88, 012116 (2013) · 5 pages, 2 figures
arxiv created 2013/07/19 · arxiv updated 2013/07/22
Utilizing operational dynamic modeling [Phys. Rev. Lett. 109, 190403 (2012); arXiv:1105.4014], 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.