Skip to main content
SpringerLink
Log in

Self-adjointness of quadratic Hamiltonians and a representation method for their exponents

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

Solutions to a series of Cauchy problems for an equation of Schrödinger type with the Hamiltonian obtained by Wiener-Segal-Fock quantization of (finite- and infinite-dimensional) Hamiltonian systems with quadratic Hamiltonians are studied. Necessary conditions for essential self-adjointness of quantum Hamiltonians considered in the paper are obtained on special domains as a corollary.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Kupsch and O. G. Smolyanov, “Asymptotic Decoherence in Infinite-Dimensional Quantum Systems with Quadratic Hamiltonians,” Matem. Zametki 73, 143 (2003) [Math. Notes 73, 136 (2003)].

    MathSciNet  Google Scholar 

  2. J. Kupsch, “The role of Infrared Divergence for Decoherence,” J. Math. Phys. 41, 5945 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  3. I. D. Tveritinov, “Asymptotic Decoherence in Quantum Systems,” Russ. J. Math. Phys. 10, 487 (2003).

    MATH  MathSciNet  Google Scholar 

  4. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1, (Mir, Moscow, 1977; Acad. Press, 1972).

    Google Scholar 

  5. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2, (Mir, Moscow, 1978; Acad. Press, 1975).

    MATH  Google Scholar 

  6. J. Kupsch, and O. G. Smolyanov, “Realization of Unitary Transformations Generating the Bogolyubov Transformations in Spaces of the Wiener-Segal-Fock Type,” Doklady Akad. Nauk 371(1), 21 (2000) [Doklady Math. 61, 169 (2000)]

    MathSciNet  Google Scholar 

  7. I. D. Tveritinov, “Bogolyubov Transformations Corresponding to Symplectic Transformations,” Vestn. Mosk. Univ., Matem. Mekhan., No. 4, 9 (2002) [Moscow Univ. Math. Bulletin, No. 4, 8 (2002)]

  8. J. Kupsch and O. G. Smolyanov, “Bogolyubov Transformations in Wiener-Segal-Fock space,” Matem. Zametki 68, 474 (2000)

    MathSciNet  Google Scholar 

  9. V. I. Bogachev, Gaussian Measures (Moscow, Nauka, 1999; AMS, Mathematical Surveys and Monographs, 1998).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    I. D. Tveritinov

Authors
  1. I. D. Tveritinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © I.D. Tveritinov, 2007, published in Vestnik Moskovskogo Universiteta, Matematika, Mekhanika, 2007, Vol. 62, No. 2, pp. 3–11.

About this article

Cite this article

Tveritinov, I.D. Self-adjointness of quadratic Hamiltonians and a representation method for their exponents. Moscow Univ. Math. Bull. 62, 41–49 (2007). https://doi.org/10.3103/S0027132207020015

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132207020015

Keywords

Search

Navigation