European Journal of Physics

Quaternion quantum mechanical treatment of an electron in a magnetic field

W Gough

Published Jul 1, 1987• 15 citations

Abstract

The energy eigenvalues and eigenfunctions of an electron in a uniform magnetic field are derived using relativistic quantum theory with a quaternion formulation.

DOI: 10.1088/0143-0807/8/3/002

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European Journal of Physics

Quaternion quantum mechanical treatment of an electron in a magnetic field

W Gough

Published Jul 1, 1987• 15 citations

Publisher

Abstract

The energy eigenvalues and eigenfunctions of an electron in a uniform magnetic field are derived using relativistic quantum theory with a quaternion formulation.

DOI: 10.1088/0143-0807/8/3/002

Related papers

Quaternionic Electron Theory: Dirac's Equation

Stefano De Leo, Waldyr A. Rodrigues

We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$ -complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$ -complex geometry is overcome by a nice ``trick'' which allows to avoid the Dirac algebra constraints in formulating our relativistic equation. A brief comparison with other quaternionic formulations is also presented.We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a nice ``trick'' which allows to avoid the Dirac algebra constraints in formulating our relativistic equation. A brief comparison with other quaternionic formulations is also presented.

arXiv:hep-th/9806057Jun 6, 19984 citations

Quantum States of a Relativistic Charged Particle in Crossed Electric and Magnetic Fields

B. A. Kagali, Tavarekere Shivalingaswamy

The exact eigenvalues and eigenfunctions of a spinless relativistic charged particle are obtained here. The results are compared with those from classical mechanics.

Mapana Journal of SciencesJul 1, 20210 citations

Increasing Quantum Speed Limit of Relativistic Electron via Non-uniform Magnetic Field

Srishty Aggarwal, Banibrata N. Mukhopadhyay, Subhashish Banerjee +2 more

Astrophysics and space science proceedingsJan 1, 20250 citations

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Maǧallaẗ ǧāmiʻaẗ Karbalāʼ/Maǧallaẗ ǧāmiʻaẗ karbalāʼJan 1, 20100 citations

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Liping Zou, Pengming Zhang, Alexander J Silenko

arXiv:2003.04717Journal of Physics G Nuclear and Particle PhysicsFeb 28, 202012 citations

The Quantum-Mechanical Description of a Relativistic Electron in a Constant and Homogeneous Magnetic Field.

David Allyn White

Jan 1, 19720 citations

We perform a one-dimensional complexified quaternionic version of the Dirac equation based on

i

-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with

i

-complex geometry is overcome by a nice ``trick'' which allows to avoid the Dirac algebra constraints in formulating our relativistic equation. A brief comparison with other quaternionic formulations is also presented.