Formal Similarity Between Mathematical Structures of Electrodynamics and Quantum Mechanics

A. A. Deriglazov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that the Schrödinger equation admits an analogous treatment. We present a Lagrangian theory of a real scalar field ø whose equation of motion turns out to be equivalent to the Schrödinger equation with time independent potential. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics. The field ø is in the same relation to the real and imaginary part of a wave function as the vector potential is in respect to electric and magnetic fields. Preservation of quantum-mechanics probability is just an energy conservation law of the field ø.

Original languageEnglish
Pages (from-to)654-662
Number of pages9
JournalInternational Journal of Theoretical Physics
Volume50
Issue number3
DOIs
Publication statusPublished - 1 Jan 2011
Externally publishedYes

Fingerprint

Electrodynamics
electrodynamics
Quantum Mechanics
quantum mechanics
Vector Potential
Electric Field
Magnetic Field
electromagnetism
electric fields
Energy Conservation
energy conservation
conservation laws
Maxwell's equations
magnetic fields
Maxwell equation
Wave Function
Preservation
Conservation Laws
Scalar Field
Equations of Motion

Keywords

  • Electrodynamics
  • Shrodinger equation

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Mathematics(all)

Cite this

Formal Similarity Between Mathematical Structures of Electrodynamics and Quantum Mechanics. / Deriglazov, A. A.

In: International Journal of Theoretical Physics, Vol. 50, No. 3, 01.01.2011, p. 654-662.

Research output: Contribution to journalArticle

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