{"title":"A Class of Stochastic and Distributions-Free Quantum Mechanical Evolution Equations","authors":"Gregorio Jose Costanza","doi":"10.12743/quanta.v10i1.159","DOIUrl":null,"url":null,"abstract":"A procedure allowing to construct rigorously discrete as well as continuum deterministic evolution equations from stochastic evolution equations is developed using Dirac's bra–ket notation. This procedure is an extension of an approach previously used by the author coined Discrete Stochastic Evolution Equations. Definitions and examples of discrete as well as continuum one-dimensional lattices are developed in detail in order to show the basic tools that allow to construct Schrödinger-like equations. Extension to multi-dimensional lattices are studied in order to provide a wider exposition and the one-dimensional cases are derived as special cases, as expected. Some variants of the procedure allow the construction of other evolution equations. Also, using a limiting procedure, it is possible to derive the Schrödinger equation from the Schrödinger-like equations. Another possible approach is given in the appendix.Quanta 2021; 10: 22–33.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quanta","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12743/quanta.v10i1.159","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
引用次数: 0
Abstract
A procedure allowing to construct rigorously discrete as well as continuum deterministic evolution equations from stochastic evolution equations is developed using Dirac's bra–ket notation. This procedure is an extension of an approach previously used by the author coined Discrete Stochastic Evolution Equations. Definitions and examples of discrete as well as continuum one-dimensional lattices are developed in detail in order to show the basic tools that allow to construct Schrödinger-like equations. Extension to multi-dimensional lattices are studied in order to provide a wider exposition and the one-dimensional cases are derived as special cases, as expected. Some variants of the procedure allow the construction of other evolution equations. Also, using a limiting procedure, it is possible to derive the Schrödinger equation from the Schrödinger-like equations. Another possible approach is given in the appendix.Quanta 2021; 10: 22–33.
QuantaArts and Humanities-History and Philosophy of Science
CiteScore
1.30
自引率
0.00%
发文量
5
审稿时长
12 weeks
期刊介绍:
Quanta is an open access academic journal publishing original research and review articles on foundations of quantum mechanics, mathematical physics and philosophy of science.