### 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 language | English |
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Pages (from-to) | 654-662 |

Number of pages | 9 |

Journal | International Journal of Theoretical Physics |

Volume | 50 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2011 |

Externally published | Yes |

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### Keywords

- Electrodynamics
- Shrodinger equation

### ASJC Scopus subject areas

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

### Cite this

*International Journal of Theoretical Physics*,

*50*(3), 654-662. https://doi.org/10.1007/s10773-010-0589-6

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

Research output: Contribution to journal › Article

*International Journal of Theoretical Physics*, vol. 50, no. 3, pp. 654-662. https://doi.org/10.1007/s10773-010-0589-6

}

TY - JOUR

T1 - Formal Similarity Between Mathematical Structures of Electrodynamics and Quantum Mechanics

AU - Deriglazov, A. A.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

KW - Electrodynamics

KW - Shrodinger equation

UR - http://www.scopus.com/inward/record.url?scp=78751703984&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78751703984&partnerID=8YFLogxK

U2 - 10.1007/s10773-010-0589-6

DO - 10.1007/s10773-010-0589-6

M3 - Article

VL - 50

SP - 654

EP - 662

JO - International Journal of Theoretical Physics

JF - International Journal of Theoretical Physics

SN - 0020-7748

IS - 3

ER -