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Letters in Mathematical Physics

, Volume 18, Issue 1, pp 43–53 | Cite as

P-adic Schrödinger-type equation

  • V. S. Vladimirov
  • I. V. Volovich
Article

Abstract

A Schrödinger-type equation is considered in relation to p-adic quantum mechanics. We discuss the appropriate notion of differential operators. A solution of the Schrödinger-type equation is given and a new set of vacuum states for the p-adic quantum harmonic oscillator is presented. The correspondence principle with the standard quantum mechanics is also discussed.

AMS subject classification (1980)

81C99 

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References

  1. 1.
    VladimirovV. S. and VolovichI. V., Theor. Math. Fiz. 59, 3 (1984); Volovich, I. V., Classical Quantum Gravity 4, L83 (1987); Lett. Math. Phys. 16, 61 (1988); Grossman, B., Phys. Lett. B197, 101 (1987); Freund, P. G. O. and Olson, M., Phys. Lett. B199, 186 (1987); Nucl. Phys. B297, 86 (1988); Freund, P. G. O. and Witten, E., Phys. Lett. B199, 191 (1987); Aref'eva, I. Ya., Dragovic, B., and Volovich, I. V., Phys. Lett. B200, 512 (1988); B209, 445 (1988); B212, 283 (1988); Frampton, P. and Okada, Y., Phys. Rev. Lett. 60, 484 (1988); Phys. Rev. D37, 3077 (1988); Gervais, J.-L., Phys. Lett. B201, 306 (1988); Marinary, E. and Parisi, G., Phys. Lett. B203, 52 (1988); Yamakoshi, H., Phys. Lett. B207, 426 (1988); Thiran, E., Verstegen, D., and Weyers, J., Preprint UCL-ITP-88-12 (1988).Google Scholar
  2. 2.
    VladimirovV. S. and VolovichI. V., Dokl. Acad. Nauk USSR 302 No. 2, 320 (1988); P-adic quantum mechanics, Commun. Math. Phys. (to be publ.).Google Scholar
  3. 3.
    Volovich, I. V., Number theory as the ultimate physical theory, Preprint CERN-TH.4981/81 (1987).Google Scholar
  4. 4.
    Alacoque, C., Ruelle, P., Thiran, E., Verstegen, D., and Weyers, J., Preprint UCL-IPT-88-05 (1988).Google Scholar
  5. 5.
    VladimirovV. S., Usp. Math. Nauk 43 No. 5, 17 (1988).Google Scholar
  6. 6.
    Aref'evaI. Ya. and VolovichI. V., Strings, gravity and p-adic space-time, in M.Markov, V.Beresin, and V.Frolov (eds), Quantum Gravity. Proceedings of the Fourth Seminar on Quantum Gravity, Moscow, 25–29 May 1987, World Scientific, Singapore, 1988, pp. 409–422.Google Scholar
  7. 7.
    ParisiG., Mod. Phys. Lett. A3, 639 (1988).Google Scholar
  8. 8.
    ZhangR. B., Phys. Lett. B209, 229 (1988).Google Scholar
  9. 9.
    SpokoinyB. L., Phys. Lett. B208, 401 (1988).Google Scholar
  10. 10.
    Okada, Y. and Ubriaco, M. R., University of North Carolina at Chapel Hill Report No. IFP-320-UNC (1988).Google Scholar
  11. 11.
    VladimirovV. S. and VolovichI. V., Vacuum state in p-adic quantum mechanics, Phys. Lett. B217, 411 (1989).Google Scholar
  12. 12.
    Zelenov, E., Theor. Math. Phys. 80 (1989).Google Scholar
  13. 13.
    Vladimirov, V. S., P-adic analysis and p-adic quantum mechanics, Ann. New York Acad. Sci., Symposium on Frontier of Mathematics, 1988 (to be published).Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • V. S. Vladimirov
    • 1
  • I. V. Volovich
    • 2
  1. 1.Steklov Mathematical InstituteMoscowUSSR
  2. 2.The Niels Bohr InstituteUniversity of CopenhagenCopenhagen ØDenmark

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