Equations of Relativistic and Quantum Mechanics and Exact Solutions of Some Problems

Mekhitarian, V. M.

doi:10.3103/s1068337218010012

Cited by 3 publications

(5 citation statements)

References 13 publications

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“…As can be seen from these equations, the action of potentials on a particle does not depend on whether the particle is moving or at rest. However, according to the NTEM, it is presumed that this action depends on the particle speed (V. J. J. o. C. P. Mekhitarian, 2012Mekhitarian, , 2018; V. J. Q. M. L. I. Mekhitarian, 2020) so that instead of 𝜙 and 𝑨 in equations (1), it is necessary to use their Lorentz transformations ' and A', given by the wellknown formulas…”

Section: General Equationsmentioning

confidence: 99%

“…Naturally, along with NTE, a new theory of magnetic interactions (NTM) must be developed; together they will form a general new theory of electromagnetic interactions (NTEM). The foundations of this general theory were laid and studied by 𝑉. Mekhitarian in pioneering works (V. J. J. o. C. P. Mekhitarian, 2012Mekhitarian, , 2018; V. J. Q. M. L. I. Mekhitarian, 2020), where electric and magnetic interactions were considered using both classical and quantum descriptions.…”

Section: Introductionmentioning

confidence: 99%

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New Classical Relativistic Theory of a Charged Particle in an Electric Field

Karapetyan

2024

Int. J. Fundam. Phys. Sci

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A new relativistic theory of the classical motion of a charged particle in an electric field has been developed. The resulting equations characterize the kinematic and dynamic features of particle motion, demonstrating peculiar behavior in areas with high attractive potentials. This changes the existing paradigm for the interaction of charge with an electric field, entailing profound consequences. The new theory converges with the conventional theory of electricity under conditions of low potentials and nonrelativistic particle velocities. The possibility of experimental verification of the new theory is discussed.

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Section: General Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Classical Relativistic Theory of a Charged Particle in an Electric Field

Karapetyan

2024

Int. J. Fundam. Phys. Sci

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“…We consider the following one-dimensional stationary relativistic wave equation (RWE) for a spinless particle of mass m and energy E in the potential field ( ) V x [1]:…”

Section: The Relativistic Wave Equation and The Schrödinger Equationmentioning

confidence: 99%

“…Constructing the spectrum for equation (1) for the case of wave functions vanishing both in the origin and at the infinity, by substitution of ( 16) into ( 14) and taking into account the physical representation (17) of the inverse-square-root potential, we obtain…”

Section: Energy Spectrum For the Inverse-square-root Potentialmentioning

confidence: 99%

“…We consider the bi-confluent Heun potentials for a stationary relativistic wave equation for a spinless particle (RWE) [1]. This equation, which is obtained by applying the invariance principle for the total four-dimensional momentum of the system "field+particle", has some significant advantages as compared to its analog equations such as the Klein-Gordon and Dirac equations [2,3].…”

Section: Introductionmentioning

confidence: 99%

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Bi-Confluent Heun Potentials for a Stationary Relativistic Wave Equation for a Spinless Particle

et al. 2018

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The variety of bi-confluent Heun potentials for a stationary relativistic wave equation for a spinless particle is presented. The physical potentials and energy spectrum of this wave equation are related to those for a corresponding Schrödinger equation in the sense that all the potentials derived for the latter equation are also applicable for the wave equation under consideration. We show that in contrast to the Schrödinger equation the characteristic spatial length of the potential imposes a restriction on the energy spectrum that directly reflects the uncertainty principle. Studying the inverse-square-root bi-confluent Heun potential, it is shown that the uncertainty principle limits, from below, the principal quantum number for the bound states, i.e., physically feasible states have an infimum cut so that the ground state adopts a higher quantum number as compared to the Schrödinger case.

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Spinor Fields

Mekhitarian¹

2023

Recent Topics and Innovations in Quantum Field Theory

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A spinor representation of the generalized energy-momentum density 4-vector is proposed, and examples of such representations for various particles and fields are given. This representation corresponds to the classical representation of the particle’s own rotation, which is described by the diagonal matrix of the moment of inertia. The concept of self-angular rotation of a particle is defined as a spatial characteristic of the field, at each point of which there is a local vortex rotation with an angular velocity Ω – a spinor field. The matrix representation of the vortex rotation Ω (spinor) and the values of the components of such a representation are derived from the matrix representation of the Lorentz transformation. The traditional concept of spin-orbit interaction, as the interaction of the magnetic moment of a particle with the magnetic field of orbital motion, is presented as the interaction of a charged particle with a spinor field. Solutions to the problems of particle motion in an external spinor field in the case of a hydrogen-like atom and planetary motion, splitting of the electron energy levels of an atom in an external magnetic field, deflection of a photon by the gravitational field, and representations in metric spaces are presented.

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Equations of Relativistic and Quantum Mechanics and Exact Solutions of Some Problems

Cited by 3 publications

References 13 publications

New Classical Relativistic Theory of a Charged Particle in an Electric Field

New Classical Relativistic Theory of a Charged Particle in an Electric Field

Bi-Confluent Heun Potentials for a Stationary Relativistic Wave Equation for a Spinless Particle

Spinor Fields

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