Open AccessA Class of Stochastic and Distributions-Free Quantum Mechanical Evolution Equations
Author(s) -
G. Costanza
Publication year - 2021
Publication title -
quanta
Language(s) - English
Resource type - Journals
ISSN - 1314-7374
DOI - 10.12743/quanta.v10i1.159
Subject(s) - notation , extension (predicate logic) , mathematics , construct (python library) , class (philosophy) , limiting , simultaneous equations , schrödinger equation , schrödinger's cat , master equation , quantum , algebra over a field , pure mathematics , mathematical physics , computer science , mathematical analysis , physics , differential equation , quantum mechanics , arithmetic , artificial intelligence , mechanical engineering , engineering , programming language
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.