Schwartz分布空间中大质量粒子的相对论自由Schrödinger方程

IF 2.2 3区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Symmetry-Basel Pub Date : 2023-10-27 DOI:10.3390/sym15111984
David Carfí
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引用次数: 0

摘要

在这项工作中,我们在缓和的分布空间中提出并解决了Schrödinger在1925年提出的一个开放问题。特别地,在Schwartz分布空间上,我们定义了与大质量粒子的相对论哈密顿算子相关的线性连续量子算子——静止质量不等于0的粒子在四维闵可夫斯基向量空间M4中演化。换句话说,在调质分布状态空间S ' (M4,C)上,我们找到了引入自由粒子相对论哈密顿算子及其对应的Schrödinger方程(以及它的共轭方程,代表反粒子)的最自然的方法。通过完全解一个缓变分布空间的除法问题,得到了相对论性线性连续演化方程的整个解空间。我们将hamilton算子(Schwartz可对角化)定义为严格正的、Schwartz可对角化的二阶微分算子(与缓变分布空间S4 '上的“Klein-Gordon算子”相联系)的主平方根。Schwartz非缺陷算子的主平方根在论文中以一种直接的方式定义——遵循一些经典的、非常有效的量子理论方法的启发式方式。
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Relativistic Free Schrödinger Equation for Massive Particles in Schwartz Distribution Spaces
In this work, we pose and solve, in tempered distribution spaces, an open problem proposed by Schrödinger in 1925. In particular, on the Schwartz distribution spaces, we define the linear continuous quantum operators associated with relativistic Hamiltonians of massive particles—particles with rest mass different from 0 and evolving in the four-dimensional Minkowski vector space M4. In other words, upon the tempered distribution state-space S′(M4,C), we have found the most natural way to introduce the free-particle relativistic Hamiltonian operator and its corresponding Schrödinger equation (together with its conjugate equation, standing for antiparticles). We have found the entire solution space of our relativistic linear continuous evolution equation by completely solving a division problem in tempered distribution space. We define the Hamiltonian (Schwartz diagonalizable) operator as the principal square root of a strictly positive, Schwartz diagonalizable second-order differential operator (linked with the “Klein–Gordon operator” on the tempered distribution space S4′). The principal square root of a Schwartz nondefective operator is defined in a straightforward way—following the heuristic fashion of some classic and greatly efficient quantum theoretical approach—in the paper itself.
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来源期刊
Symmetry-Basel
Symmetry-Basel MULTIDISCIPLINARY SCIENCES-
CiteScore
5.40
自引率
11.10%
发文量
2276
审稿时长
14.88 days
期刊介绍: Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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