广义不确定性原理的统一方法

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

Reports on Mathematical Physics Pub Date : 2024-02-01 DOI:10.1016/S0034-4877(24)00010-7

Afzal Raghavi, Ramazan Ali Mohammadian, Saeed Mohammadi

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引用次数: 0

摘要

在这项工作中，对广义不确定性原理的一些现有方案进行了回顾，并表明所有这些方案都可以通过一种统一的方法推导出来，这种方法既能保证最小可测量长度的存在，又能保证最大可用动量的存在。然后，我们提出了一个新方案，以弥补以往模型的缺陷。我们还研究了这种修改对简单谐振子能级和波函数的影响。研究表明，对于谐振子，广义不确定性关系会导致振子频率和质量之间的不确定性关系。

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A unified approach to the generalized uncertainty principle

In this work, some of the present scenarios for the generalized uncertainty principle are reviewed and it is shown that all of them could be derived through a unified approach that guarantees the existence of both, minimal measurable length and maximal available momentum. Then, a new proposal is introduced that compensates for the defects of previous models. We also studied the effects of this modification on the energy levels and the wave function of a simple harmonic oscillator. It is shown that for the case of a harmonic oscillator, generalized uncertainty relation results in an uncertainty relation between the frequency and the mass of the oscillator.

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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.