ON BOUNDARY CONDITIONS AND THE RIGGED HILBERT SPACE FORMALISM OF QUANTUM MECHANICS

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

Reports on Mathematical Physics Pub Date : 2023-04-01 DOI:10.1016/S0034-4877(23)00025-3

Nadia Boudi, Zakariae Ennadifi

引用次数: 0

Abstract

We discuss canonical rigged Hilbert space constructions. We focus on cyclic self-adjoint operators and use the one-dimensional free Hamiltonian on the half-line as a model. We propose a nonstandard construction that can be generalized to many quantum systems. Our construction is motivated by the Stone–von Neumann uniqueness theorem.

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量子力学的边界条件和操纵希尔伯特空间形式

我们讨论正则操纵希尔伯特空间结构。我们关注循环自伴随算子，并使用半线上的一维自由哈密顿算子作为模型。我们提出了一个可以推广到许多量子系统的非标准结构。我们的构造是由Stone-von Neumann唯一性定理驱动的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.