|

Computer Simulation Dynamics of the Build-up of a Singl-Slit Diffraction Pattern Using Pseudorandom-Number Generator

Authors: Neustroev A.L., Romanova T.N., Skuybin B.G. Published: 03.12.2014
Published in issue: #6(57)/2014  
DOI:

 
Category: Physics  
Keywords: diffraction pattern, diffractive distribution of probabilities, computer simulation, algorithm of pseudorandom-number generation

Shows the possibility of computer simulation important in quantum theory of the process offormation of the diffraction pattern by microparticles passing through wall with single slit. The wave-particle duality of the microparticles is one offundamental principles of the quantum mechanics. This principle is most evident in viewing experiments on dynamics of the build-up of a diffraction pattern when microparticle passes through opaque wall with single or multiple slits. The first comprehensive research and justification of correct simulation capability for dynamics of the buildup of a diffraction pattern on an example of the screen with a single slit are performed using a pseudorandom-number generator. An algorithm of generation is developed and computer program based on this algorithm is implemented. This computer program allows generating pseudorandom-number sequence with a distribution density which coincides with the distribution density for the microparticles within the diffraction pattern.

References

[1] Jonsson C. Electron diffraction at multiple slits. Am. J. Phys., 1974, vol. 42, no. 1, pp. 4-11. DOI: dx.doi.org/10.1119/1.1987592

[2] Crease R.P. The most Beautiful Experiment. Physics World, 2002, vol. 15, no. 9, pp. 19-20.

[3] Merly P.G., Missiroli G.F., Pozzi G. On the statistical aspect of electron interference phenomena. Am. J. Phys., 1974, vol. 44, no. 3, pp. 306-307. DOI: dx.doi.org/10.1119/1.10184

[4] Tonomura A., Endo J., Matsuda T., Kawasaki T., Ezawa H. Demonstration of singleelectron buildup of an interference pattern. Am. J. Phys., 1989, vol. 57, no. 2, pp. 117120. DOI: dx.doi.org/10.1119/1.16104

[5] Garcia N., Saveliev I.G., Sharonov M. Time-resolved diffraction and interference: Young’s interference with photons of different energy as revealed by time resolution. Roy. Soc. of London Phil. Tr. A, 2002, vol. 360, no. 5, pp. 1039-1059. DOI: 10.1098/rsta.2001.0980

[6] Dimitrova T.L., Weis A. The wave-particle duality of light: a demonstration experiment. Am. J. Phys., 2008, vol. 76, no. 2, pp. 137-142. DOI: dx.doi.org/10.1119/1.2815364

[7] Juffmann T., Milic A., Mullneritsch M. Real-time single-molecule imaging of quantum interference. Nature Nanotech., 2012, vol. 7, no. 5, pp. 297-300. DOI: 10.1038/nnano.2012.34

[8] Landau L.D., Lifshits E.M. Teoreticheskaja fizika. V 10 t. T. 3. Kvantovaya mekhanika [Theoretical physics. Ten-volume set. Vol. 3. Quantum Mechanics]. Moscow, Fizmatlit Publ., 2004. 800 p. (Eng. Ed.: Landau L.D., Lifshitz E.M. Quantum Mechanics: Non-Relativistic Theory. Vol. 3. Course of Theoretical Physics S. 2nd Ed. Oxford, Pergamon Press, 1965. 615 p.).

[9] Landau L.D., Lifshits E.M. Teoreticheskaja fizika. V 10 t. T. 2. Teoriya polya [Theoretical physics. Ten-volume set. Vol. 3. The Classical Theory of Fields]. Moscow, Fizmatlit Publ., 2003. 536 p. (Eng. Ed.: Landau L.D., Lifshitz E.M. The Classical Theory of Fields. Vol. 2. Course of Theoretical Physics S. 2nd ed. Oxford, Pergamon Press, 1959. 387 p.).

[10] Matveev A.N. Optika [The optics]. Moscow, Vysshaya Shkola Publ., 1985. 351 p.

[11] Law A.M., Kelton W.D. Simulation modeling and analysis. 3rd ed. McGraw Hill Higher Education, 2000. 784 p. (Russ. Ed.: Kel’ton V., Lou A. Imitatsionnoe modelirovanie. Klassika CS. SPb, Piter Publ., 2004. 848 p.).

[12] Abramowitz M., Stegun I. Handbook of mathematical functions with formulas, graphs, and mathematical tables. The U.S. National Bureau of Standards, 1964. 1046 p. (Russ. Ed.: Abramovits M., Stigan I. Spravochnik po spetsial’nym funktsiyam. Moscow, Nauka Publ., 1979. 732 p.).

[13] Rekomendatsii po standartizatsii RF R 50.1.037-2002. Prikladnaya statistika. Pravila proverki soglasiya opytnogo raspredeleniya s teoreticheskim. Ch. II. Neparametricheskie kriterii. [Recommendations for standardization RF Р 50.1.0372002. Applied statistics. Rules of check of experimental and theoretical distribution of the consent. Part II. Nonparametric goodness-of-fit test.]. Moscow, Izd. Standartov Publ., 2002. 64 p.

[14] Bol’shev L.N., Smirnov N.V. Tablitsy matematicheskoy statistiki [Tables of Mathematical Statistics]. Moscow, Nauka Publ., 1983. 416 p.