Next Article in Journal
Cohen Macaulayness and Arithmetical Rank of Generalized Theta Graphs
Next Article in Special Issue
Sharing of Nonlocality of a Single Member of an Entangled Pair of Qubits Is Not Possible by More than Two Unbiased Observers on the Other Wing
Previous Article in Journal
Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay
Previous Article in Special Issue
Entropic Uncertainty Relations for Successive Generalized Measurements
Article

Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia
Academic Editors: Takayuki Miyadera, Paul Busch and Teiko Heinosaari
Mathematics 2016, 4(3), 44; https://doi.org/10.3390/math4030044
Received: 3 March 2016 / Revised: 1 June 2016 / Accepted: 24 June 2016 / Published: 28 June 2016
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are represented by infinite series. This new mathematical tool allows us to build sensible discrete quantum mechanics based on the suggested differences and includes the correct canonical commutation and uncertainty relations. View Full-Text
Keywords: quantum theory; canonical commutation relation; uncertainty relations; exact discretization; finite difference quantum theory; canonical commutation relation; uncertainty relations; exact discretization; finite difference
MDPI and ACS Style

Tarasov, V.E. Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations. Mathematics 2016, 4, 44. https://doi.org/10.3390/math4030044

AMA Style

Tarasov VE. Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations. Mathematics. 2016; 4(3):44. https://doi.org/10.3390/math4030044

Chicago/Turabian Style

Tarasov, Vasily E. 2016. "Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations" Mathematics 4, no. 3: 44. https://doi.org/10.3390/math4030044

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop