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Absence of Eigenvalues in the Continuous Spectrum for Klein-Gordon Operators

Date: July 6,2021 |Hits: 420 Download PDF How to cite this paper

R. Ferreira1, F. N. Lima2,*, A. S. Ribeiro2

1Universidade de São Paulo (USP), São Paulo, SP, 05508-090, Brazil.

2GTMCOQ, Instituto Federal do Piauí (IFPI), São Raimundo Nonato, Piauí, 64770-000, Brazil.

*Corresponding author: F. N. Lima


We construct the one-dimensional analogous of von-Neumann Wigner potential to the relativistic Klein-Gordon operator, in which is defined taking asymptotic mathematical rules in order to obtain existence conditions of eigenvalues embedded in the continuous spectrum. Using our constructed potential, we provide an explicit and analytical example of the Klein-Gordon operator with positive eigen-values embedded in the so called relativistic “continuum region”. This result is analogous to the found in non-relativistic case for Schrodinger’s operator. Even so, in this not standard example, we present the region of the “continuum” where those eigenvalues cannot occur. Besides, the absence of eigenvalues in the continuous spectrum for Klein-Gordon operators is proven to a broad general potential classes, including the minimally coupled electric Coulomb potential. Considering known techniques available in literature for Schrodinger operators, we demonstrate an expression for Klein-Gordon operator written in Schrodinger’s form, whereby is determined the mathematical spectrum region of absence of eigenvalues.


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How to cite this paper

Absence of Eigenvalues in the Continuous Spectrum for Klein-Gordon Operators

How to cite this paper: R. Ferreira, F. N. Lima, A. S. Ribeiro. (2021) Absence of Eigenvalues in the Continuous Spectrum for Klein-Gordon Operators. Journal of Applied Mathematics and Computation5(3), 145-153.

DOI: http://dx.doi.org/10.26855/jamc.2021.09.001

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