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Ural Radio Engineering Journal

Applicability of the quantum-mechanical analogue of the uncertainty function of Woodward’s radar signal for corpuscular-wave properties of microparticles study

Stanislav N. Darovskikh, Дмитрий Сергеевич Пискорский, Д. Г. Фомин, Игорь Игоревич Прокопов

Published Dec 25, 2025• 0 citations

Abstract

The article discusses the possibility of using a quantum-mechanical analogue of the uncertainty function of the Woodward radar signal to study the corpuscular-wave properties of microparticles. The Heisenberg uncertainty relation is proved by using the uncertainty function of the Woodward radar signal. The possibility of studying the properties of a flow of microparticles with a variable momentum on its basis is demonstrated. It is proved that there is a mechanism for its “compression” in the propagation medium. Its peculiarity is in the concentration of all the energy of the sequence of microparticles within one under certain conditions. If the total energy of such the sequence is greater than the value of the potential barrier, then this particle will overcome this barrier after «compression» of the entire wave packet. No «tunnel» is required for it. The validity of using the «uncertainty function» algorithm in quantum-mechanical systems allows creating electronic devices with specified properties for various areas of their application.

DOI: 10.15826/urej.2025.9.4.004

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The article discusses the possibility of using a quantum-mechanical analogue of the uncertainty function of the Woodward radar signal to study the corpuscular-wave properties of microparticles. The Heisenberg uncertainty relation is proved by using the uncertainty function of the Woodward radar signal. The possibility of studying the properties of a flow of microparticles with a variable momentum on its basis is demonstrated. It is proved that there is a mechanism for its “compression” in the propagation medium. Its peculiarity is in the concentration of all the energy of the sequence of microparticles within one under certain conditions. If the total energy of such the sequence is greater than the value of the potential barrier, then this particle will overcome this barrier after «compression» of the entire wave packet. No «tunnel» is required for it. The validity of using the «uncertainty function» algorithm in quantum-mechanical systems allows creating electronic devices with specified properties for various areas of their application.

In radar analysis there exists an analogue of the Heisenberg uncertainty principle of quantum mechanics. Quantum mechanics stands here for the quantum-mechanical description, at a given instant of time, of a non-relativistic particle. These uncertainty principles suggest that there should exist a common mathematical structure behind both quantum mechanics and the theory of signals. It is the aim of the present article to establish that the concept of real Heisenberg nilpotent group Ã(ℝ) lies at the foundations of both of these fields. The crucial point is to endow the time-frequency plane ℝ ⊕ ℝ with the structure of a two dimensional real symplectic vector space so that it gets symplectomorphic to the tangent plane to the “Schrodinger coadjoint orbit” at the point 1 in the Kirillov orbit picture for the unitary dual of Ã(ℝ). Various applications of this geometric relationship between signal theory and nil potent harmonic analysis are pointed out. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The principle of uncertainty is one of the essential principles of quantum mechanics as it outlines that there is a reflective limit to the measurement of microscopic particle motion. However it is impossible to measure at once and accurately both the position and momentum data of any microscopic particle no matter what means are used to do so. This paper starts by discussing the notion and mathematical derivation of the uncertainty principle as put forth by Heisenberg explaining the physical relevance of the principle. It introduces the natural uncertainty the principle introduces to the dynamics of particles in the microscopic world, and the significant part it plays in the theory of quantum mechanics. The article overviews the explanations of the principle on phenomena including atomic stability and scanning tunneling microscopes, and the interference of measurement actions on the states of particles and the shortcomings of measurement precision. According to the wave-particle duality of quantum mechanics, this article gives a required theoretical basis of microscopic phenomena. Likewise, the use of the research theory on the uncertainty principle by distinguished scholars in the physics fraternity helps the readers in achieving the knowledge in related subjects more easily.

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