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Phase shifts and the modified and møller wave operators

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Abstract

The Schrödinger operator H=−Δ+V is considered when the potential V is central, oscillating and possibly unbounded. An eigenfunction expansion for H is derived. Also, the phase shift of the generalized eigenfunctions of H is computed. The expansion and shift are, together, applied to the study of the wave operators of scattering theory. The modified wave operators, for H and H 0=−Δ are shown to exist and be complete and a condition on V is derived which is necessary and sufficient for the Møller wave operators to exist and be complete. Spectral properties of H are also discussed.

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References

  1. Reed, M. and Simon, B., Methods in Modern Mathematical Physics, Vol. 3, Academic Press, New York, 1979, pp. 54–74.

    Google Scholar 

  2. Reed, M. and Simon, B., Methods in Modern Mathematical Physics, Vol. 4, Academic Press, New York, 1978, pp. 166–178.

    Google Scholar 

  3. Amrein, W.O. and Pearson, D.B., J. Physics A13, 1259 (1980).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. Ben-Artzi, M. and Devinatz, A., J. Math. Phys. 20, 594 (1979).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. Devinatz, A., J. Math. Phys. 21, 2406 (1980).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. Dollard, J.D. and Friedman, C.N., Ann. Physics 111, 251 (1978).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Hörmander, L., Math. Z. 146, 69 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  8. Ikebe, T. and Isozaki, H., Publ. Res. Inst. Math. Sci. 15, 679 (1979).

    MATH  MathSciNet  Google Scholar 

  9. White, D.A.W., Dissertation, Northwestern University (1980).

  10. VonNeumann, J. and Wigner, E., Z. Physik 30, 445 (1929).

    Google Scholar 

  11. Skriganov, M.M., J. Soviet Math. 8, 464 (1977).

    Article  MATH  Google Scholar 

Download references

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Author notes

  1. D. A. W. White

    Present address: Department of Mathematics, California Institute of Technology, 91125, Pasadena, California, USA

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  1. Stanford University, 94305, Stanford, California, USA

    D. A. W. White

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  1. D. A. W. White
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White, D.A.W. Phase shifts and the modified and møller wave operators. Lett Math Phys 6, 167–173 (1982). https://doi.org/10.1007/BF00403268

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  • DOI: https://doi.org/10.1007/BF00403268

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