Skip to main content
SpringerLink
Log in

New face of Ramsauer–Townsend effect by using a Quaternionic double Dirac potential

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

In this article, we have studied scattering of non-relativistic particles from Quaternionic double Dirac delta potential. This scattering is investigated in Quaternionic version of quantum mechanics which is based of quaternions. Probability current density functions, reflection and transmission coefficients for different regions have been calculated analytically and conservation law of probability has been checked. Then an analogy is presented between derived results and Ramsauer–Townsend effect.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. D Finkelstein, J M Jauch, S Schiminovich and D Speiser J. Math. Phys. 3 207 (1962)

    Article  ADS  Google Scholar 

  2. D Finkelstein, J M Jauch and D Speiser J. Math. Phys. 4 136 (1963)

    Article  ADS  Google Scholar 

  3. S L Adler Quaternion Quantum Mechanics and Quantum Field (New York: Oxford University Press) (1995)

    Google Scholar 

  4. A Razon and L P Horwitz Act. Appl. Math. 24 141 (1991)

    Article  Google Scholar 

  5. L P Horwitz J. Math. Phys. 34 3405 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  6. B de Witt and A Van Proyen Comm. Math. Phys. 149 307 (1992)

    Article  ADS  Google Scholar 

  7. S De Leo and P Rotelli Nuovo. Cimento. B 110 33 (1995)

    Article  ADS  Google Scholar 

  8. S L Adler Nucl. Phys. B 415 195 (1994)

    Article  ADS  Google Scholar 

  9. S De Leo Prog. Theor. Phys. 94 1109 (1995)

    Article  ADS  Google Scholar 

  10. J Rembielin’ski J. Phys. A 11 2323 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  11. L P Horwitz and L C Biedenharn Ann. Phys. 157 432 (1984)

    Article  ADS  Google Scholar 

  12. S De Leo and G Scolarici J. Phys. A. 33 2971 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  13. S De Leo, G Scolarici and L Solombrino J. Math. Phys. 43 5815 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  14. S De Leo and G Ducati J. Phys. Math. 42 2236 (2001)

    Article  Google Scholar 

  15. A J Davies and B H McKellar Phys. Rev. A 40 4209 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  16. A J Davies and B H McKellar Phys. Rev. A 46 3671-3675 (1992)

    Article  ADS  Google Scholar 

  17. S De Leo, G Ducati and C Nishi J. Phys. A 35 5411 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  18. A Peres Phys. Rev. Lett. 42 683 (1979)

    Article  ADS  Google Scholar 

  19. H Kaiser, E A George and S A Werner Phys. Rev. A 29 2276 (1984)

    Article  ADS  Google Scholar 

  20. A G Klein Phys. B 151 44 (1988)

    Article  Google Scholar 

  21. N Konno Math. Found. 2 63 (2016)

    Google Scholar 

  22. P R Girard Eur. J. Phys. 5 25 (1984)

    Article  Google Scholar 

  23. K Shoemake Comput. Graph. 19 245 (1985)

    Article  Google Scholar 

  24. S Altmann Rotations Quaternions and Double Groups (Claredon Oxford ) (1986)

    MATH  Google Scholar 

  25. M Gogberashvili Eur. Phys. J. C. 74 3200 (2014)

    Article  ADS  Google Scholar 

  26. S Gasiorowicz Quantum Physics (2003)

  27. N F Moot and H S W Massey The theory of atomic collision, 3rd edn. (London: Oxford University Press) Chapter 18 (1965)

  28. R B Brode Rev. Mod. Phys. 5 257 (1933)

    Article  ADS  Google Scholar 

  29. L I Schiff Quantum Mechanics (New York: McGraw-Hill Book Co) (1955)

    MATH  Google Scholar 

  30. E Merzbacher Quantum Mechanics (New York: John Wiley and Sons Inc) (1955)

    MATH  Google Scholar 

  31. D Bohm Quantum Theory (New York, United States) (1989)

  32. A Messiah Quantum Mechanics (Amsterdam: North-Holland Publ Co) (1961)

  33. R M Eisberg Fundamentals of Modern Physics (New York: John Wiley and Sons Inc) (1961)

    MATH  Google Scholar 

  34. S G Kukolich Am. J. Phys. 36 701 (1968)

    Article  ADS  Google Scholar 

  35. T L John J. Phys. B At. Mol. Opt. Phys. 31 65 (1998)

    Article  ADS  Google Scholar 

  36. F A Gianturco and K Willner Phys. Rev. A 75 062714 (2007)

    Article  ADS  Google Scholar 

  37. J Vahedi, K Nozari and P Pedram Grav. Cos. 18 211 (2012)

    Article  ADS  Google Scholar 

  38. L T Sin Fai Lim J. Phys. B 15 119 (1982)

    Article  ADS  Google Scholar 

  39. N F Shulga and VI Truten Phys. Lett. A 264 412 (2000)

    Article  ADS  Google Scholar 

  40. W R Hamilton Elements of Quaternions (New York: Chelsea) (1969)

    Google Scholar 

  41. W R Hamilton The Mathematical Papers of Sir William Rowan Hamilton (Cambridge: Cambridge University Press) (1967)

    MATH  Google Scholar 

  42. A A Albert Ann. of Math. 43 161 (1942)

    Article  MathSciNet  Google Scholar 

  43. B A A Rosenfeld History of Non-Euclidean Geometry (Springer) (1988)

  44. C Kevin App. Math. Comp. 84 (1) 27 (1997)

    Article  Google Scholar 

  45. A A Pogoruy and R M R Rodrígues-Dagnino Adv. in App. Clifford Algebras 20 79 (2010)

    Article  Google Scholar 

  46. J Lambek Math. Intell. 17 (4) 7 (1995)

    Article  Google Scholar 

  47. H Sobhani and H Hassanabadi Can. J. Phys. 94 (3) 262 (2016)

    Article  ADS  Google Scholar 

  48. A N Ikot, H Hassanabadi, N Salehi, H P Obong and M C Onyeaju Ind. J. Phys. 89, 11 1221 (2015)

Download references

Author information

Authors and Affiliations

  1. Young Researchers and Elite Club, Damghan Branch, Islamic Azad University, Damghan, Iran

    Hadi Sobhani

  2. Physics Department, Shahrood University of Technology, P.O.Box: 3619995161-316, Shahrood, Iran

    Hassan Hassanabadi

Authors
  1. Hadi Sobhani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hassan Hassanabadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hadi Sobhani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sobhani, H., Hassanabadi, H. New face of Ramsauer–Townsend effect by using a Quaternionic double Dirac potential. Indian J Phys 91, 1205–1209 (2017). https://doi.org/10.1007/s12648-017-1010-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-017-1010-6

Keywords

PACS Nos.

Search

Navigation