On the invariance properties of the Klein-Gordon equation with external electromagnetic field

A simple method for generating the exact solutions of the nonlinear Klein–Gordon equation is proposed. The solutions obtained depend on two arbitrary functions and are in the form of running waves. An application of one of the solutions for the (2 + 1) – dimensional sine-Gordon equation is proposed. It concerns the selective properties of a two-dimensional semi-infinite Josephson junction with regard to an external electromagnetic field in the form of running waves with a phase velocity equal to the Swihart velocity. A method for measuring the Swihart velocity is presented.

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HIGHER-DIMENSIONAL GEOMETRIC DESCRIPTION OF THE QUANTUM KLEIN–GORDON EQUATION

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887813200144 ◽

2013 ◽

Vol 10 (09) ◽

pp. 1320014 ◽

Cited By ~ 3

Author(s):

BENJAMIN KOCH

Keyword(s):

Electromagnetic Field ◽

Gordon Equation ◽

Bohmian Mechanics ◽

External Electromagnetic Field ◽

Geometrical Theory ◽

Geometric Description ◽

Curved Space ◽

Higher Dimensional ◽

Klein Gordon ◽

Klein Gordon Equation

It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum mechanics as a purely classical geometrical theory. The results are further generalized to interactions with an external electromagnetic field.

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Mechanics of a charged particle on the Kaluza–Klein background

Canadian Journal of Physics ◽

10.1139/p95-087 ◽

1995 ◽

Vol 73 (9-10) ◽

pp. 602-607 ◽

Cited By ~ 2

Author(s):

S. R. Vatsya

Keyword(s):

Electromagnetic Field ◽

Charged Particle ◽

Integral Method ◽

Gordon Equation ◽

Type Equation ◽

Fifth Dimension ◽

Klein Gordon ◽

Path Integral Method ◽

Klein Gordon Equation ◽

Kaluza Klein

The path-integral method is used to derive a generalized Schrödinger-type equation from the Kaluza–Klein Lagrangian for a charged particle in an electromagnetic field. The compactness of the fifth dimension and the properties of the physical paths are used to decompose this equation into its infinite components, one of them being similar to the Klein–Gordon equation.

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SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS

Reviews in Mathematical Physics ◽

10.1142/s0129055x02001168 ◽

2002 ◽

Vol 14 (04) ◽

pp. 409-420 ◽

Cited By ~ 189

Author(s):

VIERI BENCI ◽

DONATO FORTUNATO FORTUNATO

Keyword(s):

Electromagnetic Field ◽

Solitary Wave ◽

Electric Field ◽

Solitary Waves ◽

Maxwell Equations ◽

Gordon Equation ◽

Klein Gordon ◽

Klein Gordon Equation

This paper is divided in two parts. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. In the second part we study the electrostatic case. We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ.

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Electromagnetic interaction with the Klein–Gordon equation in the framework of GUP

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887821501991 ◽

2021 ◽

Vol 18 (12) ◽

Author(s):

B. Khosropour

Keyword(s):

Magnetic Field ◽

Electromagnetic Field ◽

Uncertainty Principle ◽

Electric Potential ◽

Uniform Magnetic Field ◽

Gordon Equation ◽

Electromagnetic Interaction ◽

Generalized Uncertainty Principle ◽

Klein Gordon ◽

Klein Gordon Equation

In this work, according to the generalized uncertainty principle, we study the Klein–Gordon equation interacting with the electromagnetic field. The generalized Klein–Gordon equation is obtained in the presence of a scalar electric potential and a uniform magnetic field. Furthermore, we find the relation of the generalized energy–momentum in the presence of a scalar electric potential and a uniform magnetic field separately.

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