Skip to main content
SpringerLink
Log in

Monodromy-free Schrödinger operators with quadratically increasing potentials

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider one-dimensional monodromy-free Schrödinger operators with quadratically increasing rational potentials. It is shown that all these operators can be obtained from the operator -∂2 + x2 by finitely many rational Darboux transformations. An explicit expression is found for the corresponding potentials in terms of Hermite polynomials.

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. J. Duistermaat and F. A. Grünbaum,Commun. Math. Phys.,103, 177 (1986).

    Article  MATH  ADS  Google Scholar 

  2. O. A. Chalykh,Russ. Math. Surv.,53, 377 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  3. Yu. Yu. Berest and A. P. Veselov,Russ. Math. Surv.,53, 208 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  4. V. M. Goncharenko and A. P. Veselov,J. Phys. A,31, 5315 (1998).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. G. Darboux,Comp. Rend. Acad. Sci.,94, 1343 (1882).

    Google Scholar 

  6. J. L. Burchnall and T. W. Chaundy,Proc. London Math. Soc. Ser. 2,21, 420 (1930).

    Article  Google Scholar 

  7. M. M. Crum,Quart. J. Math. Oxford. Ser. 2,6, 121 (1955).

    Article  MATH  MathSciNet  Google Scholar 

  8. E. L. Ince,Ordinary Differential Equations, Dover Publications, New York (1944).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. A. Oblomkov

Authors
  1. A. A. Oblomkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 3, pp. 374–386, December, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Oblomkov, A.A. Monodromy-free Schrödinger operators with quadratically increasing potentials. Theor Math Phys 121, 1574–1584 (1999). https://doi.org/10.1007/BF02557204

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02557204

Keywords

Search

Navigation