Skip to main content
Log in

Asymptotics of Information Entropy for the Two-Dimensional Analog of the Relativistic Hydrogen Atom in the Kozlov-Nikishin Model

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

For the two-dimensional Lorentz-invariant model of the hydrogen atom, we obtain wave functions of bound states in coordinate representation and, for nonexcited (in time) states, also in momentum representation. For such states, the short-wave asymptotics of the information entropy is studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. I. Bialynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics,” Cumm. Math. Phys., 44 (1975), 129–132.

    MathSciNet  Google Scholar 

  2. J. S. Dehesa, R. J. Yanez, and A. I. Aptekarev, and V. Buyarov, “Strong asymptotics of Laguerre polynomials and information entropies of the two-dimensional harmonic oscillator and one-dimensional Coulomb potentials,” J. Math. Phys., 39 (1998), no. 6, 3050–3060.

    Article  MathSciNet  Google Scholar 

  3. R. J. Yanez and W. Van Assche, and J. S. Dehesa, “Position and momentum information entropies of the D-dimensional harmonic oscillator and hydrogen atom,” Phys. Rev. A, 50 (1994), 3065–3079.

    Google Scholar 

  4. J. S. Dehesa and A. Martinez-Finkelshtein, and V. N. Sorokin, “Quantum-information entropies for highly excited states of single-particle systems with power-type potentials,” Phys. Rev. A, 66 (2002), 2109.

    Article  Google Scholar 

  5. J. S. Dehesa and A. Martinez-Finkelshtein, and V. N. Sorokin, “Asymptotics of information entropies of some Toda-like potentials,” J. Math. Phys., 44 (2003), no. 1, 36–47.

    Article  MathSciNet  Google Scholar 

  6. V. V. Kozlov and E. M. Nikishin, “A relativistic version of Hamiltonian formalism and the wave functions of the hydrogenlike atom,” Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.] (1986), no. 5, 11–20.

  7. V. V. Kozlov, “The relativistic many-body problem and its quantization,” in: Selected Questions of Mathematical Analysis (E. M. Nikishin, editor) [in Russian], Dokl. Math. Appl., vol. 3, no.1, Moscow-Tula, 1990, pp. 430–431.

  8. V. A. Fock, Works in Quantum Field Theory [in Russian], Izd. Leningrad Univ., Leningrad, 1957. AU: Flugge,-Siegfried TI: Practical quantum mechanics. I, II. NT: Die Grundlehren der mathematischen Wissenschaften, Bande 177 und 178. PY: 1971 PUBL: Springer-Verlag, Berlin-New York, 1971

    Google Scholar 

  9. S. Flugge, Practical Quantum Mechanics, vols. I and II, Die Grundlehren der mathematischen Wissenschaften, Bande 177 und 178, Springer-Verlag, Berlin-New York, 1971; Russian translation: Mir, Moscow, 1974.

    Google Scholar 

  10. A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics [in Russian], 2nd ed., Nauka, Moscow, 1984.

    Google Scholar 

  11. H. Bateman and A. Erdelyi, Higher Transcendental Functions, vols. 1–3, McGraw-Hill, New York-Toronto-London, 1953–1955; Russian translation: Nauka, Moscow, 1965.

    Google Scholar 

  12. A. I. Aptekarev, V. S. Buyarov, and J. S. Deheza, “The asymptotic behavior of the L p-norms and entropy for general orthogonal polynomials,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 82 (1995), 373–395.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Matematicheskie Zametki, vol. 78, no. 5, 2005, pp. 727–744.

Original Russian Text Copyright ©2005 by M. A. Prikhod'ko.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Prikhod'ko, M.A. Asymptotics of Information Entropy for the Two-Dimensional Analog of the Relativistic Hydrogen Atom in the Kozlov-Nikishin Model. Math Notes 78, 677–692 (2005). https://doi.org/10.1007/s11006-005-0171-3

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11006-005-0171-3

Key words

Navigation