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Event Based Interpretation of Schrödinger’s Equation for the Two-slit Experiment

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Abstract

A discrete time event based model is constructed for particles emitted one-at-a-time in the two slit experiment of quantum mechanics. It is shown that the simulations of the model align with the solutions of the time-dependent non-relativistic Schrödinger’s equation corresponding to the experiment. The event based model provides an interpretation of the two slit experiment as the aggregate behaviour of individual particles, whose paths are probabilistically differentiated according to sequential rules for their discrete spatial movements in time.

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References

  1. Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics, vol. 3. Addison-Wesley, Reading (1965)

    MATH  Google Scholar 

  2. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 41, 777–780 (1935)

    Article  ADS  Google Scholar 

  3. Born, M.: Zur Quantenmechanik der Stoßvorgänge (Quantum mechanics of collision). Z. Phys. 38, 803–827 (1926)

    Article  ADS  Google Scholar 

  4. Popper, K.R.: Quantum mechanics without the “observer”. In: Bunge, M. (ed.) Quantum Theory and Reality, pp. 1–12. Springer, New York (1967)

    Google Scholar 

  5. Lande, A.: New Foundations of Quantum Mechanics. Cambridge University Press, London (1965)

    MATH  Google Scholar 

  6. Lande, A.: Quantum Mechanics in a New Key. Exposition Press, New York (1973)

    Google Scholar 

  7. Ballentine, L.E.: The statistical interpretation of quantum mechanics. Rev. Mod. Phys. 41, 074401 (1970)

    Google Scholar 

  8. Ballentine, L.E.: Quantum Mechanics: A Modern Development, pp. 358–380. World Scientific, Singapore (1998)

    MATH  Google Scholar 

  9. Einstein, A.: Albert Einstein: Philosopher-Scientist. Cambridge University Press, London (1949)

    Google Scholar 

  10. McClendon, M., Rabitz, H.: Numerical simulations in stochastic mechanics. Phys. Rev. A 37, 3479–3492 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  11. Marcella, T.: Quantum interference with slits. Eur. J. Phys. 23, 615–621 (2002)

    Article  MATH  Google Scholar 

  12. Kato, T.: Perturbation Theory for Linear Operators. Springer, New York (1966)

    MATH  Google Scholar 

  13. Goldstein, J.A.: Semigroups of Linear Operators and Applications. Oxford University Press, Oxford (1990)

    Google Scholar 

  14. Dyson, J., Villella-Bressan, R., Webb, G.F.: A nonlinear age and maturity structured model of population dynamics. II. Chaos. J. Math. Anal. Appl. 242, 255–270 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. De Raedt, H., De Raedt, K., Michielsen, K., Keimpema, K., Miyashita, S.: Event-based computer simulation model of aspect-type experiments strictly satisfying Einstein’s locality conditions. J. Phys. Soc. Jpn. 76, 104005 (2007)

    Article  ADS  Google Scholar 

  16. Zhao, S., Yuan, S., De Raedt, H., Michielsen, K.: Computer simulations of Wheeler’s delayed-choice experiment with photons. Europhys. Lett. 82, 40004 (2008)

    Article  ADS  Google Scholar 

  17. De Raedt, H., Zhao, S., Yuan, S., Jin, S., Michielsen, K., Miyashita, S.: Event-by-event simulation of quantum phenomena. Physica E, Low-Dimens. Syst. Nanostruct. 42, 298–302 (2010)

    Article  ADS  Google Scholar 

  18. Jin, F., Yuan, S., De Raedt, H., Michielsen, K., Miyashita, S.: Corpuscular model of two-beam interference and double-slit experiments with single photons. J. Phys. Soc. Jpn. 79, 074401 (2010)

    Article  ADS  Google Scholar 

  19. Mermin, N.D.: What is quantum mechanics trying to tell us? Am. J. Phys. 66, 753–767 (1998)

    Article  ADS  Google Scholar 

  20. Tonomura, A., Endo, J., Matsuda, T., Kawasaki, T.: Demonstration of single-electron buildup of an interference pattern. Am. J. Phys. 102, 14952–14959 (1989)

    Google Scholar 

  21. Hongo, H., Miyamoto, Y., Furuya, K., Suhara, M.: A 40-nm-pitch double-slit experiment of hot electrons in a semiconductor under a magnetic field. Appl. Phys. Lett. 70, 93–95 (1997)

    Article  ADS  Google Scholar 

  22. Tonomura, A.: The Quantum World Unveiled by Electron Waves. World Scientific, Singapore (1998)

    Book  Google Scholar 

  23. Arndt, M., Nairz, O., Vos-Andreae, J., Keller, C., van der Zouw, G., Zeilinger, A.: Wave particle duality of C 60 molecules. Nature 401, 680–682 (1999)

    Article  ADS  Google Scholar 

  24. Nairz, O., Arndt, M., Zeilinger, A.: Quantum interference experiments with large molecules. Am. J. Phys. 71, 319–325 (2003)

    Article  ADS  Google Scholar 

  25. Tonomura, A.: Direct observation of thitherto unobservable quantum phenomena by using electrons. Proc. Natl. Acad. Sci. USA 57, 107–120 (2005)

    Google Scholar 

  26. Barrachina, R.O., Frémont, F., Gruyer, D., Helaine, V., Lepailleur, A., Leredde, A., Maclot, S., Scamps, G., Chesnel, J.-Y.: Linewidth oscillations in a nanometer-size double-slit interference experiment with single electrons. Phys. Rev. A 81, 060702 (2010)

    Article  ADS  Google Scholar 

  27. Gloge, D., Marcuse, D.: Formal quantum theory of light rays. J. Opt. Soc. Am. 59, 1629–1631 (1969)

    Article  ADS  Google Scholar 

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  1. Department of Mathematics, Stevenson Center, Vanderbilt University, Nashville, TN, 37240, USA

    G. F. Webb

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  1. G. F. Webb
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Correspondence to G. F. Webb.

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Webb, G.F. Event Based Interpretation of Schrödinger’s Equation for the Two-slit Experiment. Int J Theor Phys 50, 3571–3601 (2011). https://doi.org/10.1007/s10773-011-0866-z

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  • DOI: https://doi.org/10.1007/s10773-011-0866-z

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