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Intelligent Mathematics II: Applied Mathematics and Approximation Theory pp 73–85Cite as

Spinning Particle in Interaction with a Time Dependent Magnetic Field: A Path Integral Approach

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 441))

Abstract

We consider a spin 1 / 2 particle interacting with a time dependent magnetic field using path integral formalism. The propagator is first of all written in the standard form by replacing the spin by two fermionic oscillators via the Schwinger’s model; then it is determined exactly thanks to a simple transformations and the probability transition is then deduced.

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References

  1. Aouachria, M., Chetouani, L.: Rabi oscillations in gravitational fields: exact solution via path integral. Eur. Phys. J. C 25, 333–338 (2002)

    Article  MATH  Google Scholar 

  2. Aouachria, M., Chetouani, L.: Treatment of a damped two-level atom in an electromagnetic wave by the path integral formalism. Chin. J. Phys. 40, 496–504 (2002)

    Google Scholar 

  3. Aouachria, M.: Spin coherent state path integral for a two-level atom in an electromagnetic wave of circular polarization. Chin. J. Phys. 49, 689–698 (2011)

    Google Scholar 

  4. Aouachria, M.: Rabi oscillation in a damped rotating magnetic field: a path integral approach. J. Phys. Conf. Ser. 435, 012021 (2013)

    Article  Google Scholar 

  5. Barut, A.O., Beker, H.: Exact Solutions of spin (Rabi) precession, transmission and reflection in the Eckhart potential. Eur. Phys. Lett. 14, 197–202 (1991)

    Article  MathSciNet  Google Scholar 

  6. Boudjedaa, T., Bounames, A., Nouicer, Kh, Chetouani, L., Hammann, T.F.: Path integral for the generalized Jaynes-Cummings model. Phys. Scr. 54, 225–233 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Boudjedaa, T., Bounames, A., Nouicer, Kh, Chetouani, L., Hammann, T.F.: Coherent state path integral for the interaction of spin with external magnetic fields. Phys. Scr. 56, 545–554 (1998)

    Article  MATH  Google Scholar 

  8. Calvo, M., Codriansky, S.: A class of solvable Pauli-Schrödinger hamiltonians. J. Math. Phys. 24, 553–559 (1983)

    Google Scholar 

  9. Codriansky, S., Cordero, P., Salamo, S.: On a class of solvable Pauli-Schrödinger hamiltonians. Z. Phys. A 353, 341–343 (1995)

    Article  Google Scholar 

  10. Grosche, C., Steiner, F.: Handbook of Feynman Path Integrals. Springer, Berlin (1998)

    MATH  Google Scholar 

  11. Lämmerzahl, C., Bordé, C.J.: Rabi oscillations in gravitational fields: exact solution. Phys. Lett. A 203, 59–67 (1995)

    Article  Google Scholar 

  12. Merdaci, A., Boudjedaa, T., Chetouani, L.: Exact path Integral for neutral spinning particle in interaction with helical magnetic field. Phys. Scr. 64, 15–19 (2001)

    Article  MATH  Google Scholar 

  13. Merdaci, A., Boudjedaa, T., Chetouani, L.: Path integral for a neutral spinning particle in interaction with a rotating magnetic field and a scalar potential. Czech. J. Phys. 51, 865–881 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Merdaci, A., Boudjedaa, T., Chetouani, L.: A neutral spinning particle in interaction with a magnetic field and Poschl-Teller potential. Eur. Phys. J. C 22, 585–592 (2001)

    Article  MATH  Google Scholar 

  15. Mijatović, M., Ivanovski, C., Veljanoski, B., Trenčevski, K.: Scattering and bound states of a nonrelativistic neutral spin-1/2 particle in a magnetic field. Z. Phys. A 345, 65–77 (1993)

    Article  Google Scholar 

  16. Nakamura, M., Kazuo Kitahara, K.: Spin depolarization of a quantum particle; fermionic path integral approach. J. Phys. Soc. Jpn. 60, 1388–1397 (1991)

    Google Scholar 

  17. Nouicer, Kh, Chetouani, L.: Path integral approach to the supersymmetric generalized Jaynes-Cummings model. Phys. Lett. A 281, 218–230 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Qiong-Gui, L.: Exact solutions for neutral particles in the field of a circularly polarized plane electromagnetic wave. Phys. Lett. A 342, 67–76 (2005)

    Article  Google Scholar 

  19. Rabi, I.I.: Space quantization in a gyrating magnetic field. Phys. Rev. 51, 652–654 (1937)

    Article  MATH  Google Scholar 

  20. Tahmasebi, M.J., Sobouti, Y.: Exact solutions of Schrödinger’s equation for spin systems in a class of time-dependent magnetic fields. Mod. Phys. Lett. B 5, 1919–1924 (1991)

    Google Scholar 

  21. Tahmasebi, M.J., Sobouti, Y.: Exact solutions of Schrödinger’s equation for spin systems in a class of time-dependent magnetic fields II. Mod. Phys. Lett. B 6, 1255–1261 (1992)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Hadj lakhdar, Batna, Algeria

    Hilal Benkhelil & Mekki Aouachria

Authors
  1. Hilal Benkhelil
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  2. Mekki Aouachria
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Correspondence to Mekki Aouachria .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee, USA

    George A. Anastassiou

  2. Department of Mathematics, TOBB Economics and Technology University, Ankara, Turkey

    Oktay Duman

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Benkhelil, H., Aouachria, M. (2016). Spinning Particle in Interaction with a Time Dependent Magnetic Field: A Path Integral Approach. In: Anastassiou, G., Duman, O. (eds) Intelligent Mathematics II: Applied Mathematics and Approximation Theory. Advances in Intelligent Systems and Computing, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-319-30322-2_5

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  • DOI: https://doi.org/10.1007/978-3-319-30322-2_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30320-8

  • Online ISBN: 978-3-319-30322-2

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