Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations

Mathematics

卷:4

Vasily E. Tarasov¹ 

[1] Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia;

关键词: quantum theory;    canonical commutation relation;    uncertainty relations;    exact discretization;    finite difference;   

DOI  :  10.3390/math4030044

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown