Mathematical models for the common features of quantum scale and normal scale phenomena

Catalin Silviu Nutu

doi:10.1117/12.2322531

31 December 2018 Mathematical models for the common features of quantum scale and normal scale phenomena

Catalin Silviu Nutu

Proceedings Volume 10977, Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies IX; 109772B (2018) https://doi.org/10.1117/12.2322531
Event: Advanced Topics in Optoelectronics, Microelectronics and Nanotechnologies IX, 2018, Constanta, Romania

Abstract

The aim of the paper is to seek and identify mathematical models designated to understand better the quantum scale phenomena, models which could permit to link them with the real world phenomena. This shall be made by analyzing the common features exhibited by both, normal scale and quantum scale phenomena and then, by creating mathematical models that are describing both, the quantum and the real world. One main idea of the paper, on which the involved models are built is that observed physical quantities such as position and momentum of a quantum particle, but also the laws of their transformation (of that physical quantities) from one state into another such as for example the probability wave function described by the Schrödinger’s equation, are signals transmitted out of the quantum world into the real physical world by the a certain real, not yet detected wave function, wave function, underlying the visible measurable reality and which is describing this more complex reality underlying the observable one, and unavailable not only to our limited senses but also not available, even though using the new discovered technologies. The two observed physical quantities, position and momentum, are describing a quantum system, that is to say the quantum system can be represented either as a wave function of the position of the particle or as a wave function of the momentum of the particle, this two different functions being linked one to another by means of the Fourier Transform. The paper is furthermore describing the way in which the theory of Signal Processing, a powerful and useful tool, is to be used in order to model both, quantum and large scale phenomena.

Citation Download Citation

Catalin Silviu Nutu "Mathematical models for the common features of quantum scale and normal scale phenomena", Proc. SPIE 10977, Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies IX, 109772B (31 December 2018); https://doi.org/10.1117/12.2322531

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KEYWORDS

Signal processing

Particles

Quantum physics

Linear filtering

Fourier transforms

Mathematical modeling

Detection theory

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