Exact discrete analogs of canonical commutation and uncertainty relations
type: Item
instance of: scholarly article
title: Exact discrete analogs of canonical commutation and uncertainty relations
zbMATH Open document ID: 1360.39006
author: Vasily E. Tarasov
published in: Mathematics
publication date: 2017-03-16T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 81S05
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 6695467
zbMATH Keywords: quantum theory
zbMATH Keywords: canonical commutation relation
zbMATH Keywords: uncertainty relations
zbMATH Keywords: exact discretization
zbMATH Keywords: finite difference
MaRDI profile type: Publication
full work available at URL: math4030044
OpenAlex ID: W2470544856
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DOI: 10.3390/MATH4030044
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description: scientific article; zbMATH DE number 6695467