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Singular continuous measures in scattering theory

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Abstract

Examples are presented of potentialsV for which −d 2 /dr 2+V(r) inL 2(0, ∞) has singular continuous spectrum, and the physical interpretation is discussed.

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References

  1. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  2. Amrein, W., Georgescu, V.: Helv. Phys. Acta46, 635–658 (1973)

    Google Scholar 

  3. Wilcox, C.: J. Funct. Anal.12, 257–274 (1973)

    Google Scholar 

  4. Pearson, D.: Helv. Phys. Acta48, 639–653 (1975)

    Google Scholar 

  5. Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. I. New York-London: Academic Press 1972

    Google Scholar 

  6. Weidmann, J.: Math. Zeitschr.98, 268–302 (1967)

    Google Scholar 

  7. Lavine, R.: Indiana Univ. Math. J.21, 643–656 (1972)

    Google Scholar 

  8. Lavine, R.: J. Funct. Anal.12, 30–54 (1973)

    Google Scholar 

  9. Gel'fand, L., Levitan, B.: Am. Math. Soc. Trans.1, 253–304 (1955)

    Google Scholar 

  10. Aronszajn, N.: Am. J. Math.79, 597–610 (1957)

    Google Scholar 

  11. Coddington, E., Levinson, N.: Theory of ordinary differential equations. New York: McGraw-Hill 1955

    Google Scholar 

  12. Halmos, P.: Measure theory. Princeton: Van Norstrand 1950

    Google Scholar 

  13. Cox, D., Miller, H.: The theory of stochastic processes. London: Methuen 1965

    Google Scholar 

  14. Bartle, R.: The elements of integration. New York: Wiley 1966

    Google Scholar 

  15. Pearson, D.: Commun. math. Phys.40, 125–146 (1975)

    Google Scholar 

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Communicated by J. Ginibre

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Pearson, D.B. Singular continuous measures in scattering theory. Commun.Math. Phys. 60, 13–36 (1978). https://doi.org/10.1007/BF01609472

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  • DOI: https://doi.org/10.1007/BF01609472

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