The construction of Gel'fand triplet space structure for Infinite Potential Well System

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2023-06-01 DOI:10.1016/S0034-4877(23)00036-8

Onur Genç, Haydar Uncu

引用次数: 0

Abstract

The Hilbert space is the space which is usually chosen as the space of state vectors. In addition, the operators of quantum mechanics act on that space. However, the Hilbert space cannot provide a proper mathematical structure to define Dirac formulation. In particular, the use of Dirac formalism on the domain of definition of an observable leads to some physical contradictions. One example arises from the Infinite Potential Well System (IPWS) which is one of the most fundamental systems of quantum mechanics. Our aim in this paper is the explicit construction of the Gel'fand triplet for the IPWS.

查看原文本刊更多论文

无限大势井系统的凝胶型和三重态空间结构的构建

希尔伯特空间是通常被选择作为状态向量空间的空间。此外，量子力学的算符作用于那个空间。然而，希尔伯特空间不能提供一个合适的数学结构来定义狄拉克公式。特别地，狄拉克形式主义在可观察物的定义领域的应用导致了一些物理上的矛盾。无限势阱系统(IPWS)就是一个例子，它是量子力学中最基本的系统之一。本文的目的是明确构建IPWS的Gel’fand三元组。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.