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On relativistic energy band corrections in the presence of periodic potentials

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Abstract

A previously developed formalism to compute relativistic corrections of bound state energies for spin-1/2 particles is applied to relativistic corrections of energy bands of one-dimensional, periodic Hamiltonians. We explicitly describe Floquet theory for periodic Dirac operators on the line. Extensions including impurity potentials and/or v≥2 dimensions are straightforward and sketched at the end.

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References

  1. Avron, J., Grossmann, A., and Rodriguez, R., Rep. Math. Phys. 5, 113 (1974).

    Google Scholar 

  2. Avron, J., Grossmann, A., and Rodriguez, R., Ann. Phys. 102, 555 (1976).

    Google Scholar 

  3. Avron, J. and Simon, B., Ann. Phys. 110, 85 (1978).

    Google Scholar 

  4. Cirincione, R. J. and Chernoff, P. R., Commun. Math. Phys. 79, 33 (1981).

    Google Scholar 

  5. Deift, P. A. and Hempel, R., Commun. Math. Phys. 103, 461 (1986).

    Google Scholar 

  6. Eastham, M. S. P., The Spectral Theory of Periodic Differential Equations, Scottish Academic Press, New York, 1973.

    Google Scholar 

  7. Firsova, N. E., Theoret. Math. Phys. 62, 130 (1985).

    Google Scholar 

  8. Gesztesy, F., Grosse, H., and Thaller, B., Phys. Rev. Lett. 50, 625 (1983).

    Google Scholar 

  9. Gesztesy, F., Grosse, H., and Thaller, B., Ann. Inst. H. Poincaré 40, 159 (1984).

    Google Scholar 

  10. Hempel, R., Manuscripta Math. 48, 19 (1984).

    Google Scholar 

  11. Hempel, R., Hinz, A. M., and Kalf, H., Math. Ann. 277, 197 (1987).

    Google Scholar 

  12. Hunziker, W., Commun. Math. Phys. 40, 215 (1975).

    Google Scholar 

  13. Kato, T., Petturbation Theory for Linear Operators, 2nd edn., Springer-Verlag, New York, Berlin, 1980.

    Google Scholar 

  14. Khryashchev, S. V., J. Sov. Math. 37, 908 (1987).

    Google Scholar 

  15. Klaus, M., Helv. Phys. Acta 55, 49 (1982).

    Google Scholar 

  16. Kohn, W., Phys. Rev. 115, 809 (1959).

    Google Scholar 

  17. Reed, M. and Simon, B., Methods of Modern Mathematical Physics IV: Analysis of Operators, Academic Press, New York, 1978.

    Google Scholar 

  18. Rofe-Beketov, F. S., Sov. Math. Dokl. 5, 689 (1964).

    Google Scholar 

  19. Simon, B., Ann. Inst. H. Poincaré 24, 91 (1976).

    Google Scholar 

  20. Skriganov, M. M., Invent. Math. 80, 107 (1985).

    Google Scholar 

  21. Veselié, K., Commun. Math. Phys. 22, 27 (1971).

    Google Scholar 

  22. Veselić, K., J. Math. Anal. Appl. 96, 63 (1983).

    Google Scholar 

  23. Wiegner, A., Über den nichtrelativistischen Grenzwert der Eigenwerte der Diracgleichung, Diploma Thesis, Fernuniversität-Gesamthochschule Hagen, FRG, 1984.

  24. Zelenko, L. B., Math. Notes 20, 750 (1976).

    Google Scholar 

  25. Zheludev, V. A., Topics in Math. Phys. 4, 55 (1971).

    Google Scholar 

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Author notes

  1. F. Gesztesy (Max Kade Foundation Fellow)

    Present address: Institute for Theoretical Physics, University of Graz, A-8010, Graz, Austria

Authors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Graz, A-8010, Graz, Austria

    W. Bulla

  2. Department of Mathematics, California Institute of Technology, 91125, Pasadena, CA, USA

    F. Gesztesy (Max Kade Foundation Fellow)

  3. Institut für Theoretische Physik, Technische Universität Graz, A-8010, Graz, Austria

    K. Unterkofler

Authors
  1. W. Bulla
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  2. F. Gesztesy
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  3. K. Unterkofler
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Bulla, W., Gesztesy, F. & Unterkofler, K. On relativistic energy band corrections in the presence of periodic potentials. Lett Math Phys 15, 313–324 (1988). https://doi.org/10.1007/BF00419589

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  • DOI: https://doi.org/10.1007/BF00419589

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