Visual Analysis of Quantum Physics Data

  • Hans-Christian Hege
  • Michael Koppitz
  • Falko Marquardt
  • Chris McDonald
  • Christopher Mielack
Part of the CRM Series in Mathematical Physics book series (CRM)


During the past two decades data visualization has matured as an own sub-discipline in computer science. Its methods are successfully applied in almost all areas of science, engineering, and medicine, in order to depict and visually analyze data—both from experiment and simulation. The goal of data visualization is to achieve a better understanding of data by intuitive, perceptually efficient and interactively steerable depictions of the data. For this specific data analysis methods are combined with visualization techniques that utilize modern computer graphics. Quantum physics, however, so far remained largely omitted as application area, in particular due to the high dimensionality of the phenomena. However, the situation is not hopeless; on the contrary, there are many ways to visualize quantum mechanical phenomena. In this paper, this will be demonstrated by means of visualizations of simulation data from quantum chemistry and high-harmonic generation.


Wigner Function Visualization Technique Volume Rendering Quantum Mechanical Phenomenon Visual Data Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Brandt, H.D. Dahmen, The Picture Book of Quantum Mechanics, 3rd edn. (Springer, New York, 2001)Google Scholar
  2. 2.
    B. Thaller, Visual Quantum Mechanics (Springer, New York, 2000)Google Scholar
  3. 3.
    B. Thaller, Advanced Visual Quantum Mechanics (Springer, New York, 2005)Google Scholar
  4. 4.
    D.T. Smithey, M. Beck, M.G. Raymer, A. Faridani, Phys. Rev. Lett. 70, 1244 (1993)ADSCrossRefGoogle Scholar
  5. 5.
    J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J.C. Kieffer, P.B. Corkum, D.M. Villeneuve, Nature 432, 867 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    S. Haessler, J. Caillat, W. Boutu, C. Giovanetti-Teixeira, T. Ruchon, T. Auguste, Z. Diveki, P. Breger, A. Maquet, B. Carr´e, R. Taïeb, P. Salières, Nature Phys. 6, 200 (2010)Google Scholar
  7. 7.
    C. Figueira de Morisson Faria, B.B. Augstein, Phys. Rev. A 81, 043409 (2010)Google Scholar
  8. 8.
    H. Niikura, N. Dudovich, D.M. Villeneuve, P.B. Corkum, Phys. Rev. Lett. 105, 053003 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    J. Meyer, J. Thomas, S. Diehl, B. Fisher, D.A. Keim, in Scientific Visualization: Advanced Concepts, Dagstuhl Follow-Ups, vol. 1, ed. by H. Hagen (Schloss Dagstuhl—Leibniz-Zentrum f¨ur Informatik, Dagstuhl, 2010), pp. 227–245. URL
  10. 10.
    C.D. Hansen, C.R. Johnson, The Visualization Handbook (Academic Press, Orlando, FL, 2005)Google Scholar
  11. 11.
    A.C. Telea, Data Visualization (A K Peters Ltd, London, 2007)Google Scholar
  12. 12.
    J.L. Moreland, A. Gramada, O.V. Buzko, Q. Zhang, P.E. Bourne, BMC Bioinformatics 6, 21 (2005)CrossRefGoogle Scholar
  13. 13.
    S.J. Lee, H.Y. Chung, K.S. Kim, Bull. Kor. Chem. Soc. 25, 1061 (2004)CrossRefGoogle Scholar
  14. 14.
    J.D. Gans, D. Shalloway, J. Mol. Graph. Model. 19, 557 (2001)CrossRefGoogle Scholar
  15. 15.
    J. Schmidt-Ehrenberg, D. Baum, H.C. Hege, in VIS ’02—Proceedings of the conference on Visualization ’02 (IEEE, Washington, DC, 2002), pp. 235–242Google Scholar
  16. 16.
    F.W. Young, P. Rheingans, IBM J. Res. Develop. 35, 97 (1991)CrossRefGoogle Scholar
  17. 17.
    E.A. Rundensteiner, M.O.Ward, J. Yang, P.R. Doshi, in SIGMOD ’02 Proceedings of the 2002 ACM SIGMOD International Conference on Management of Data (ACM, New York, 2002), p. 631Google Scholar
  18. 18.
    P.E. Hoffman, G.G. Grinstein, in Information Visualization in Data Mining and Knowledge Discovery, ed. by U. Fayyad, G.G. Grinstein, A. Wierse (Morgan Kaufmann, San Francisco, CA, 2001), pp. 47–82Google Scholar
  19. 19.
    J.A. Walter, H. Ritter, in KDD ’02 - Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (ACM, New York, 2002), pp. 123–132Google Scholar
  20. 20.
    A. Hinneburg, D.A. Keim, M. Wawryniuk, IEEE Comput. Graphics Appl. 19(5), 22 (1999)CrossRefGoogle Scholar
  21. 21.
    K. Engel,M. Hadwiger, J.M. Kniss, C. Rezk-Salama, Real-Time Volume Graphics (A K Peters Ltd, London, 2006)Google Scholar
  22. 22.
    H.C. Hege, T. Höllerer, D. Stalling, Volume rendering—mathematical models and algorithmic aspects. Tech. Rep. 93–07, ZIB (1993)Google Scholar
  23. 23.
    L. Noodleman, J.G. Norman, J.H. Osborne, A. Aizman, D.A. Case, J. Am. Chem. Soc. 107(12), 3418 (1985)CrossRefGoogle Scholar
  24. 24.
    T.S. Newman, H. Yi, Computers & Graphics 30, 854 (2006)CrossRefGoogle Scholar
  25. 25.
    W.E. Lorensen, H.E. Cline, in SIGGRAPH ’87—Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, ed. by M.C. Stone (ACM, New York, 1987), pp. 163–169Google Scholar
  26. 26.
    J. Chambers, W. Cleveland, B. Kleiner, P. Tukey, Graphical Methods for Data Analysis (Wadsworth, Monterey, CA, 1983)Google Scholar
  27. 27.
    N. Elmqvist, P. Dragicevic, J.D. Fekete, IEEE Trans. Vis. Comput. Graph. 14(6), 1141 (2008)CrossRefGoogle Scholar
  28. 28.
    A. Inselberg, B. Dimsdale, in Visualization ’90—Proceedings of the 1st Conference on Visualization (IEEE, Washington, DC, 1990), pp. 361–378Google Scholar
  29. 29.
    A. Inselberg, Parallel Coordinates—Visual Multidimensional Geometry and Its Applications (Springer, New York, 2009)Google Scholar
  30. 30.
    J. Blaas, C.P. Botha, F.H. Post, IEEE Trans. Vis. Comput. Graph. 14(6), 1436 (2008)CrossRefGoogle Scholar
  31. 31.
    D. Asimov, SIAM J. Sci. Statist. Comput. 6, 128 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    H. Hauser, F. Ledermann, H. Doleisch, in INFOVIS ’02 Proceedings of the IEEE Symposium on Information Visualization (IEEE, Washington, DC, 2002), pp. 127–130Google Scholar
  33. 33.
    D. Stalling, M. Westerhoff, H.C. Hege, in The Visualization Handbook, ed. by C.D. Hansen, C.R. Johnson (Academic Press, Orlando, FL, 2005), chap. 38, pp. 749–767Google Scholar
  34. 34.
    I. Barth, H.C. Hege, H. Ikeda, A. Kenfack, M. Koppitz, J. Manz, F. Marquardt, G.K. Paramonov, Chem. Phys. Lett. 481, 118 (2009)ADSCrossRefGoogle Scholar
  35. 35.
    J. Caillat, J. Zanghellini,M. Kitzler, O. Koch,W. Kreuzer, A. Scrinzi, Phys. Rev. A 71, 012712 (2005)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Hans-Christian Hege
    • 1
  • Michael Koppitz
    • 1
  • Falko Marquardt
    • 1
    • 2
  • Chris McDonald
    • 3
  • Christopher Mielack
    • 1
  1. 1.Zuse Institute BerlinBerlinGermany
  2. 2.Department of MathematicsFU BerlinBerlinGermany
  3. 3.University of OttawaOttawaCanada

Personalised recommendations