Relativistic wave equations: an operational approach

The use of operator methods of an algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schrödinger, Klein-Gordon, a...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 48; no. 12; pp. 125203 - 17
Main Authors Dattoli, G, Sabia, E, Górska, K, Horzela, A, Penson, K A
Format Journal Article
LanguageEnglish
Published IOP Publishing 27.03.2015
Subjects
Algebra
Approximation
Differential equations
evolution operator
Mathematical models
operational methods
Operators (mathematics)
relativistic wave equations
Schroedinger equation
Wave equations
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Summary:The use of operator methods of an algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schrödinger, Klein-Gordon, and Dirac. We discuss the free-particle hypotheses and those relevant to particles subject to non-trivial potentials. In the latter case we will show how the proposed method leads to easily implementable numerical algorithms.
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/12/125203