Derivation of Dirac, Klein-Gordon, Schrödinger, diffusion and quantum heat transport equations from a universal quantum wave equation

Arbab, Arbab I.

doi:10.1209/0295-5075/92/40001

Cited by 40 publications

(47 citation statements)

References 10 publications

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“…The applications arise, for example, in the propagation of electrical signals and optimization of guided communication systems [6][7][8][9]. It is recently shown by Arbab [10] that a quaternionic momentum eigenvalue produces a telegraph equation. This equation is found to describe the propagation of a quantum particle.…”

Section: Introductionmentioning

confidence: 99%

A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations

Alawad

Yousif

Arbab

2013

International Journal of Differential Equations

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In this paper, the exact solutions of space-time fractional telegraph equations are given in terms of Mittage-Leffler functions via a combination of Laplace transform and variational iteration method. New techniques are used to overcome the difficulties arising in identifying the general Lagrange multiplier. As a special case, the obtained solutions reduce to the solutions of standard telegraph equations of the integer orders.

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Section: Introductionmentioning

confidence: 99%

A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations

Alawad

Yousif

Arbab

2013

International Journal of Differential Equations

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“…Like Maxwell's formulation, in this formulation the particle is described by scalar and vector potentials. These equations read (Arbab, 2010) …”

Section: Universal Quantum Equationsmentioning

confidence: 99%

The Modified Electromagnetism and the Emergent Longitudinal Wave

Arbab¹,

Ajmi²

2018

APR

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The classical theory of electromagnetism has been revisited and the possibility of longitudinal photon wave is explored. It is shown that the emergence of longitudinal wave is a consequence of Lorenz gauge (condition) violation. Proca, Vlaenderen & Waser and Arbab theories are investigated. The different approaches are compared to each other and the relevant equations are combined. The telegrapher's equation can be obtained and with a specific choice of the function a Klein-Gordon equation of massive scalar field can be obtained. When the Lorentz gauge is violated by introducing the first order time derivative the emergence of the photon mass and the relevant longitudinal wave for the electromagnetic wave is apparnt.

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“…It means in particular that quantum mechanics in distinction from quantum electrodynamics cannot be formulated within the frames of the quaternion theory immediately. At the same time, there are at present a number of publications, devoted just to the reformulation of quantum mechanics on the quaternion base, for instance, [20,21,22,23]. Moreover, they are very popular.…”

Section: T H R T H R T H R T H R T Imentioning

confidence: 99%

“…Let us give the concrete example of the incorrectness of the given re-formulation. The author of [20,21,22,23] has claimed on the derivation of a "universal quantum wave equation" that yields Dirac, Klein-Gordon, SchrÄodinger and quantum heat equations. However, the author itself indicates that the additional transformations are needed to agree so colled "universal quantum equation" with Dirac equation.…”

Section: T H R T H R T H R T H R T Imentioning

confidence: 99%

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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Derivation of Dirac, Klein-Gordon, Schrödinger, diffusion and quantum heat transport equations from a universal quantum wave equation

Cited by 40 publications

References 10 publications

A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations

A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations

The Modified Electromagnetism and the Emergent Longitudinal Wave

To Principles of Quantum Theory Construction

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