Skip to main content

Double-Slit Interference Pattern for a Macroscopic Quantum System

Foundations of Physics volume 46, pages 1634–1648 (2016)Cite this article

Abstract

In this study, we solve analytically the Schrödinger equation for a macroscopic quantum oscillator as a central system coupled to two environmental micro-oscillating particles. Then, the double-slit interference patterns are investigated in two limiting cases, considering the limits of uncertainty in the position probability distribution. Moreover, we analyze the interference patterns based on a recent proposal called stochastic electrodynamics with spin. Our results show that when the quantum character of the macro-system is decreased, the diffraction pattern becomes more similar to a classical one. We also show that, depending on the size of the slits, the predictions of quantum approach could be apparently different with those of the aforementioned stochastic description.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

Fig. 1
Fig. 2
Fig. 3

References

  1. Feynman, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integrals. McGraw-Hill, New York (1965)

    MATH  Google Scholar 

  2. Zecca, A.: Diffraction of Gaussian wave packets by a single slit. Eur. Phys. J. Plus 126, 18 (2011)

    Article  Google Scholar 

  3. Zecca, A.: Double slit diffraction pattern of Gaussian wave packet interacting with the wall. Adv. Stud. Theor. Phys. 1, 539 (2007)

    MathSciNet  MATH  Google Scholar 

  4. Zimmermann, B., Rolles, D., Langer, B., Hentges, R.: Localization and loss of coherence in molecular double-slit experiments. Nat. Phys. 4, 649 (2008)

    Article  Google Scholar 

  5. Nairz, O., Arndt, M., Zeilinger, Anton: Quantum interference experiments with large molecules. Am. J. Phys. 71, 319 (2003)

    Article  ADS  Google Scholar 

  6. Hornberger, K., Uttenthaler, S., Brezger, B., Hackermuller, L., Arndt, M., Zeilinger, A.: Collisional decoherence observed in matter wave interferometry. Phys. Rev. Lett. 90, 160401 (2003)

    Article  ADS  Google Scholar 

  7. Hornberger, K., Gerlich, S., Haslinger, P., Nimmrichter, S., Arndt, M.: Colloquium: quantum interference of clusters and molecules. Mod. Phys 84, 157 (2012)

    Article  ADS  Google Scholar 

  8. Gerlich, S., Eibenberger, S., Tomandl, M., Nimmrichter, S., Hornberger, K., Fagan, P.J., Tuxen, J., Mayor, M., Arndt, M.: Quantum interference of large organic molecules. Nature Comm. 2, 263 (2011)

    Article  ADS  Google Scholar 

  9. Merzbacher, E.: Quantum Mechanics. Wiely, New York (1970)

    MATH  Google Scholar 

  10. Holland, P.R.: The Quantum Theory of Motion. Cambridge University Press, New York (1993)

    Book  Google Scholar 

  11. Zecca, A.: Two-slit diffraction pattern for gaussian wave packets. Int. J. Theor. Phys. 38, 911 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zecca, A., Cavalleri, G.: Gaussian wave packets passing through a slit: a comparison between the predictions of the Schrödinger QM and of stochastic electrodynamics with spin. Nuovo Cimento 112.B, 1 (1997)

    Google Scholar 

  13. Zecca, A.: N-slit diffraction pattern. Int. J. Theor. Phys. 38, 1883 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zecca, A.: Gaussian wave packets passing through two slits: contribution of confinement and tunneling to the diffraction pattern. Adv. Studies Theor. Phys. 7, 287 (2013)

    Article  MathSciNet  Google Scholar 

  15. Cavalleri, G.: h derived from cosmology and origin of special relativity and QM. Nuovo Cimento 112.B, 1193 (1997)

    ADS  Google Scholar 

  16. Takagi, S.: Macroscopic Quantum Tunneling. Cambridge University Press, New York (2005)

    Google Scholar 

  17. McDermott, R. M., Redmount, I. H.: Coupled classical and quantum oscillators (2004). arXiv:quant-ph/0403184

  18. Cavalleri, G., Barbero, F., Bertazzi, G., Cesaroni, E., Tonni, E., Bosi, L., Spavieri, G., Gillies, G.T.: Aquantitative assessment of stochastic electrodynamics with spin (SEDS): physical principles and novel applications. Front. Phys. China 5(1), 107 (2010)

    Article  ADS  Google Scholar 

  19. Cavalleri, G., Tonni, E.: Discriminating between QM and SED with spin. In: Garola, C., Rossi, A. (eds.) The Foundations of Quantum Mechanics - Historical Analysis and Open Questions. World Scientific, Singapore (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Group on Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O.Box 11365-9516, Tehran, Iran

    Hamid Reza Naeij & Afshin Shafiee

  2. School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

    Afshin Shafiee

Authors
  1. Hamid Reza Naeij
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Afshin Shafiee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Afshin Shafiee.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Naeij, H.R., Shafiee, A. Double-Slit Interference Pattern for a Macroscopic Quantum System. Found Phys 46, 1634–1648 (2016). https://doi.org/10.1007/s10701-016-0034-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-016-0034-7

Keywords

  • Double-slit
  • Interference
  • Macroscopic quantum system
  • Stochastic electrodynamics with spin