Conceptual inconsistencies in finite-dimensional quantum and classical mechanics
arXiv:1112.3679 · doi:10.1103/PhysRevA.88.012116
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.
5 pages, 2 figures
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Cited by in corpus (6)
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- Making Distinct Dynamical Systems Appear Spectrally Identical
- Wigner-Lindblad equations for quantum friction
- Controlling Arbitrary Observables in Correlated Many-body Systems
- Entropy non-conservation and boundary conditions for Hamiltonian dynamical systems
- Operational Dynamical Modeling of spin 1/2 relativistic particles: the Dirac equation and its classical limit