English

Conceptual inconsistencies in finite-dimensional quantum and classical mechanics

Quantum Physics 2013-07-22 v2 Mathematical Physics math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.1112.3679,
  title  = {Conceptual inconsistencies in finite-dimensional quantum and classical mechanics},
  author = {Denys I. Bondar and Renan Cabrera and Herschel A. Rabitz},
  journal= {arXiv preprint arXiv:1112.3679},
  year   = {2013}
}

Comments

5 pages, 2 figures