Foundations of Physics

, Volume 46, Issue 12, pp 1634–1648 | Cite as

Double-Slit Interference Pattern for a Macroscopic Quantum System

  • Hamid Reza Naeij
  • Afshin ShafieeEmail author


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.


Double-slit Interference Macroscopic quantum system Stochastic electrodynamics with spin 


  1. 1.
    Feynman, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integrals. McGraw-Hill, New York (1965)zbMATHGoogle Scholar
  2. 2.
    Zecca, A.: Diffraction of Gaussian wave packets by a single slit. Eur. Phys. J. Plus 126, 18 (2011)CrossRefGoogle Scholar
  3. 3.
    Zecca, A.: Double slit diffraction pattern of Gaussian wave packet interacting with the wall. Adv. Stud. Theor. Phys. 1, 539 (2007)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Zimmermann, B., Rolles, D., Langer, B., Hentges, R.: Localization and loss of coherence in molecular double-slit experiments. Nat. Phys. 4, 649 (2008)CrossRefGoogle Scholar
  5. 5.
    Nairz, O., Arndt, M., Zeilinger, Anton: Quantum interference experiments with large molecules. Am. J. Phys. 71, 319 (2003)ADSCrossRefGoogle Scholar
  6. 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)ADSCrossRefGoogle Scholar
  7. 7.
    Hornberger, K., Gerlich, S., Haslinger, P., Nimmrichter, S., Arndt, M.: Colloquium: quantum interference of clusters and molecules. Mod. Phys 84, 157 (2012)ADSCrossRefGoogle Scholar
  8. 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)ADSCrossRefGoogle Scholar
  9. 9.
    Merzbacher, E.: Quantum Mechanics. Wiely, New York (1970)zbMATHGoogle Scholar
  10. 10.
    Holland, P.R.: The Quantum Theory of Motion. Cambridge University Press, New York (1993)CrossRefGoogle Scholar
  11. 11.
    Zecca, A.: Two-slit diffraction pattern for gaussian wave packets. Int. J. Theor. Phys. 38, 911 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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. 13.
    Zecca, A.: N-slit diffraction pattern. Int. J. Theor. Phys. 38, 1883 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 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)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Cavalleri, G.: h derived from cosmology and origin of special relativity and QM. Nuovo Cimento 112.B, 1193 (1997)ADSGoogle Scholar
  16. 16.
    Takagi, S.: Macroscopic Quantum Tunneling. Cambridge University Press, New York (2005)Google Scholar
  17. 17.
    McDermott, R. M., Redmount, I. H.: Coupled classical and quantum oscillators (2004). arXiv:quant-ph/0403184
  18. 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)ADSCrossRefGoogle Scholar
  19. 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

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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Research Group on Foundations of Quantum Theory and Information, Department of ChemistrySharif University of TechnologyTehranIran
  2. 2.School of PhysicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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