Skip to main content
Log in

Inverse scattering problem for one-dimensional Schrödinger operators related to the general stark effect

  • Published:
Acta Mathematicae Applicatae Sinica Aims and scope Submit manuscript

Abstract

This paper discusses the inverse scattering problem for one-dimensional Schrodinger operators related to the general Stark effect. We provide a general framework which can be applied both to the Stark-effect operator and the ordinary Schrodinger operator.

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. Li Yishen, One Special Inverse problem of the Second Order Differential Equation on the Whole Real Axis,Chin Ann. of Math.,2: 2 (1981), 146–155.

    Google Scholar 

  2. Yosida, K., Lectures on Differential and Integral Equation, Interscience, New York, 1960.

    Google Scholar 

  3. Lippman, B. A., Schwinger, J., Variational Principles for Scattering Processes,Phys. Rev.,79:3 (1950), 469–480.

    Article  Google Scholar 

  4. Richtmyer, R. D., Principles of Advanced Mathematical Physics, Vol. 1, Springer-Verlag, Berlin, 1978.

    Google Scholar 

  5. Rama Mohana Rao, M, Odinary Differential Equations, Edward Arnold, London, 1981.

    Google Scholar 

  6. Tichmarsh, E. G., Eigenfunction Expension Associated with Section Order Differential Equation, Oxford Press, London, 1958.

    Google Scholar 

  7. Schechter, M. Operator Methods in Quantum Mechanics, North Holland, New York, 1981.

    Google Scholar 

  8. Friedman, B., Principles and Techniques of Applied Mathematics, Wiley, New York, 1956.

    Google Scholar 

  9. Chambers, Li. G., Integral Equations: A Short Course, International Textbook Company Limited, London, 1976.

    Google Scholar 

  10. Graffi, S., Harrell, E., Inverse Scattering for the One—Dimensional Stark Effect and Application to the Cylindrical KdV Equation,Ann Inst. Henri Poincaré, Vol,XXXVI, No. 1, 1982, 41–58.

    Google Scholar 

  11. Coddington, E. A., and Levinson, N., Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.

    Google Scholar 

  12. Avron, J. E. and Herbst, I. W., Spectral and Scattering Theory of Schrodinger Operator Related to the Stark Effect,Commun. Math. Phys.,52 (1977), 239–254.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lin, Y., Qian, M. & Zhang, Q. Inverse scattering problem for one-dimensional Schrödinger operators related to the general stark effect. Acta Mathematicae Applicatae Sinica 5, 116–136 (1989). https://doi.org/10.1007/BF02009745

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02009745

Keywords

Navigation