Startseite Relativistic Ŝ-matrix formulation in one dimension for particles of spin-s (s = 0, 1/2)
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Relativistic Ŝ-matrix formulation in one dimension for particles of spin-s (s = 0, 1/2)

  • Nahla Bourouis , Kamel Khounfais EMAIL logo und Meheiddine Bouatrous
Veröffentlicht/Copyright: 30. Oktober 2023

Abstract

In quantum scattering theory, the time evolution of a physical system can be described as a series of unitary transformations. The operator of this transformation will be denoted S ̂ ; the corresponding matrix is the Ŝ-matrix (scattering matrix). This last object contains all the information on the broadcast process associated with the operator S ̂ The present work has two objectives: To develop the one-dimensional formalism of the scattering matrix of relativistic particles of spin-s (s = 0, 1/2) in the presence of a localized electromagnetic field on the one hand and on the other hand to analyze the solutions of the problem of scattering states of relativistic particles of spin-s in interaction with some localized scalar potentials via the S ̂ -matrix formalism.


Corresponding author: Kamel Khounfais, LRPCSI Université 20 août 1955 Skikda, BP-26, 21000 Skikda, Algeria, E-mail:

Acknowledgments

Authors strongly thank the head of the LRPCSI laboratory at the university August 20, 1955 SKIKda for their support.

  1. Research ethics: Not applicable.

  2. Author contributions: The authors has accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: The authors states no conflict of interest.

  4. Research funding: None declared.

  5. Data availability: Not applicable.

References

[1] R. G. Newton, Scattering Theory of Waves and Particles, New York Heidelberg Berlin, Springer-verlag, 1982.10.1007/978-3-642-88128-2Suche in Google Scholar

[2] F. J. Dyson, “The S matrix in quantum electrodynamics,” Phys. Rev., vol. 75, pp. 486; 1736, 1949, https://doi.org/10.1103/physrev.75.1736.Suche in Google Scholar

[3] K. Khounfais, T. Boudjedaa, and L. Chetouani, “Scattering matrix for Feshbach-Villars equation for spin 0 and 1/2: Woods–Saxon potential,” Czechoslov. J. Phys., vol. 54, no. 7, p. 697, 2004, https://doi.org/10.1023/b:cjop.0000038524.36986.19.10.1023/B:CJOP.0000038524.36986.19Suche in Google Scholar

[4] A. Wachter, Relativistic Quantum Mechanics, Berlin, Springer Science + Business Media B.V, 2011.10.1007/978-90-481-3645-2Suche in Google Scholar

[5] L. Mario and O. Benhar, Relativistic Quantum Mechanics, An Introduction to Relativistic Quantum Fields, USA, CRC Press Taylor&Francis Group, 2016.Suche in Google Scholar

[6] V. G. Bagrov and D. Gitman, The Dirac Equation And its Solutions, Berlin, Walter de Gruyter & Co, 2014.10.1515/9783110263299Suche in Google Scholar

[7] Y. Nogami and C. K. Ross, “Scattering from a nonsymmetric potential in one dimension as a coupled-channel problem,” Am. J. Phys., vol. 64, p. 923, 1996, https://doi.org/10.1119/1.18123.Suche in Google Scholar

[8] L. B. Okun, Weak Interaction of Elementary Particles, Oxford, Pergamon Press, 1965.10.1016/B978-0-08-013702-5.50009-9Suche in Google Scholar

[9] W. Greiner, Relativistic Quantum Mechanics, Berlin, Springer, 2000.10.1007/978-3-662-04275-5Suche in Google Scholar

[10] J. H. Eberly, “Quantum scattering theory in one dimension,” Am. J. Phys., vol. 33, p. 771, 1965, https://doi.org/10.1119/1.1970982.Suche in Google Scholar

[11] B. Stec and C. Jedrzejek, “Resonance scattering by a double square-well potential,” Eur. J. Phys., vol. 11, p. 75, 1990, https://doi.org/10.1088/0143-0807/11/2/002.Suche in Google Scholar

[12] C. Rojas and V. M. Villalba, “Scattering of a Klein-Gordon particle by a Woods–Saxon potential,” Phys. Rev., vol. A71, 2005, Art. no. 052101, https://doi.org/10.1103/physreva.71.052101.Suche in Google Scholar

[13] P. Kennedy, “The Woods–Saxon potential in the Dirac equation,” J. Phys. A: Math. Gen., vol. 35, pp. 689–698, 2002, https://doi.org/10.1088/0305-4470/35/3/314.Suche in Google Scholar

[14] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, New York, Dover, 1965.Suche in Google Scholar

[15] W. W. Bell, Special Functions for Scientists and Engineers, D. Van Nostrand Company Canada, Ltd, 1968.Suche in Google Scholar

Received: 2023-04-20
Accepted: 2023-10-09
Published Online: 2023-10-30
Published in Print: 2023-12-27

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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