To Principles of Quantum Mechanics Development

Yerchuck, Dmitri; Dovlatova, Alla; Borovik, F. N.; Yerchak, Yauhen; Stelmakh, V. F.

doi:10.12691/ijp-2-5-2

Cited by 2 publications

(5 citation statements)

References 38 publications

(119 reference statements)

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“…We wish also to report that recently [26] the conclusion on the status of the second main postulate of quantum mechanics was presented. The strict mathematical proof of the hypothesis of SchrÄodinger on the existence of the field scalar function, being to be observable quantity, just charge density was obtained.…”

Section: E a I A I A K A A A A Rmentioning

confidence: 99%

“…, : ' , 0 1 0 in the given representation are the Hermitian conjugates of the matrices, determined by (26), that is…”

Section: E a I A I A K A A A A Rmentioning

confidence: 99%

“…Mapping, given by (26), realizes the connection between quaternions and operators on Hilbert spaces.…”

Section: E a I A I A K A A A A Rmentioning

confidence: 99%

“…The atomic system in [26] is considered from the positions of the field theory, that is, it seems to be the association of elementary particles with corresponding fields. The given fields being to be the media for the particles' propagation are responsible for the wave aspect in the characteristics of atomic systems.…”

Section: E a I A I A K A A A A Rmentioning

confidence: 99%

“…The wave aspect is described by the independent scalar wave function which was also introduced in quantum physics by SchrÄodinger. The description of the wave aspect was developed in the work [26]. The expression for the scalar wave function, based on the boson Fermi liquid model of EM-field was derived.…”

Section: E a I A I A K A A A A Rmentioning

confidence: 99%

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To Principles of Quantum Theory Construction

Yerchuck¹,

Dovlatova²,

Alexandrov³

2014

IJP

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New insight to the principles of the quantum theory construction is given. It is based on the symmetry study of main differential equations of mechanics and electrodynamics. It has been shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered within the frames of the number theory) determine the mathematical nature of the quantities, incoming in given equations. The substantial consequence of the given consideration is the proof of the main postulate of quantum mechanics, that is, the proof of the statement, that to any quantum mechanical quantity can be set up into the correspondence the Hermitian matrix. It is shown, that a non-abelian character of the multiplicative group of the quaternion ring leads to the nonapplicability of the quaternion calculus for the construction of new versions of quantum mechanics directly. The given conclusion seems to be actual, since there is a number of modern publications with the development of the quantum mechanics theory using the quaternions with the standard basis {e, i, j, k}. The correct way for the construction of new versions of quantum mechanics on the quaternion base is discussed in the paper presented. It is realized by means of the representation of the quaternions through the basis of the linear space of complex numbers over the field of real numbers, under the multiplicative group of which the equations of the dynamics of mechanical systems are invariant. At the same time the quaternion calculus is applicable in electrodynamics, at that the new versions of quantum electrodynamics can be constructed by an infinite number of the ways corresponding to an infinite number of the matrix representations of the standard quaternion basis {e, i, j, k}. The given conclusion is the consequence of the high symmetry of Maxwell equations.

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Section: E a I A I A K A A A A Rmentioning

confidence: 99%

“…, : ' , 0 1 0 in the given representation are the Hermitian conjugates of the matrices, determined by (26), that is…”

Section: E a I A I A K A A A A Rmentioning

confidence: 99%

“…Mapping, given by (26), realizes the connection between quaternions and operators on Hilbert spaces.…”

Section: E a I A I A K A A A A Rmentioning

confidence: 99%

Section: E a I A I A K A A A A Rmentioning

confidence: 99%

Section: E a I A I A K A A A A Rmentioning

confidence: 99%

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To Principles of Quantum Theory Construction

Yerchuck¹,

Dovlatova²,

Alexandrov³

2014

IJP

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The Photon Concept and the Physics of Quantum Absorption Process

Yerchuck¹,

Yerchak²,

Dovlatova³

et al. 2015

BJAST

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The status of the photon in the modern physics was analysed. Within the frames of the Standard Model of particle physics the photon is considered to be the genuine elementary particle, being to be the messenger of the electromagnetic interaction to which are subject charged particles. In contrast, the experts in quantum electodynamics (in particular, in quantum optics) insist, that the description of an photon to be the particle is impossible. The given viewpoint was carefully analysed and its falseness was proved. The expression for a photon wave function is presented. So, the status of the photon in quantum electodynamics was restored. The physics of a quantum absorption process is analysed. It is argued in accordance with Dirac guess, that the photon revival takes place by its absorption. Being to be a soliton, it seems to be keeping safe after an energy absorption in a pinned state, possessing the only by spin. It is shown, that the time of the transfer of absorbing systems in an excited state is finite and moreover, that it can govern the stationary signal registered. The given result is significant for the all stationary spectroscopy, in which at present the transfer of absorbing systems in an excited state is considered to be instantaneous.

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To Principles of Quantum Mechanics Development

Cited by 2 publications

References 38 publications

To Principles of Quantum Theory Construction

To Principles of Quantum Theory Construction

The Photon Concept and the Physics of Quantum Absorption Process

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