High energy asymptotics for the total scattering phase in potential scattering theory

1. P. Alsholm, G. Schmidt, Spectral and scattering theory for Schrödinger operators, Arch. Rat. Mech. Anal. 40 (1971), 281–311.

   Article  MathSciNet  MATH  Google Scholar 

2. M. S. Birman, M. G. Krein, On the theory of wave operators and scattering operators, Dokl. Akad. Nauk. SSSR 144 (1962), 475–478; Soviet Math. Dokl. 3 (1962), 740–744.

   MathSciNet  Google Scholar 

3. V. S. Buslaev, Trace formulas for Schrödinger's operator in three-space, Dokl. Akad. Nauk SSSR 143 (1962), 1067–1070; Soviet Phys. Dokl. 7 (1962), 295–297.

   MathSciNet  MATH  Google Scholar 

4. V. S. Buslaev, Scattered plane waves, spectral asymptotics and trace formulas in exterior problems, Dokl. Akad. Nauk SSSR 197 (1971), 999–1002; Soviet Math. Dokl. 12 (1971), 591–595.

   MathSciNet  MATH  Google Scholar 

5. Y. Colin de Verdière, Une formule de traces pour l'opérateur de Schrödinger dansR³, Ann. Scient. Éc. Norm. Sup. 14 (1981), 27–39.

   MATH  Google Scholar 

6. L. Guillopé, Une formule de trace pour l'opérateur de Schrödinger dansRⁿ, Thèse de 3ème cycle, Grenoble, 1981.

   Google Scholar 

7. L. Guillopé, Asymptotique de la phase de diffusion pour l'opérateur de Schrödinger avec potentiel, C. R. Acad. Sc. Paris Série I 293 (1981), 601���603.

   MATH  Google Scholar 

8. L. Guillopé, Asymptotique de la phase de diffusion pour l'opérateur de Schrödinger dansRⁿ, Sem. Bony-Sjöstrand-Meyer 1984–1985, Exposé no. V.

   Google Scholar 

9. A. Jensen, A stationary proof of Lavine's formula for time-delay, Lett. Math. Phys. 7 (1983), 137–143.

   Article  MathSciNet  MATH  Google Scholar 

10. A. Jensen, T. Kato, Asymptotic behavior of the scattering phase for exterior domains, Comm. in. Partial Differential Equations, 3 (1978), 1165–1195.

    Article  MathSciNet  MATH  Google Scholar 

11. A. Jensen, T. Kato, Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. J. 46 (1979), 583–611.

    Article  MathSciNet  MATH  Google Scholar 

12. T. Kato, Growth properties of solutions of the reduced wave equation with a variable coefficient, Comm. Pure Appl. Math. 12 (1959), 403–425.

    Article  MathSciNet  MATH  Google Scholar 

13. M. G. Krein, On the trace formula in the theory of perturbation, Math. Sb. 33(75) (1953), 597–626.

    MathSciNet  Google Scholar 

14. M. G. Krein, On perturbation determinants and a trace formula for unitary and selfadjoint operators, Dokl. Akad. Nauk SSSR 144 (1962), 268–271; Soviet Math. Dokl. 3 (1962), 707–710.

    MathSciNet  Google Scholar 

15. S. T. Kuroda, Scattering theory for differential operators, I, II, J. Math. Soc. Japan 25 (1973), 75–104, 222–234.

    Article  MathSciNet  MATH  Google Scholar 

16. S. T. Kuroda, An introduction to scattering theory, Aarhus Universitet, Matematisk Institut, lecture notes series No. 51, 1978.

    Google Scholar 

17. A. Majda, J. Ralston, An analogue of Weyl's theorem for unbounded domains. I, II, and III, Duke Math. J. 45 (1978), 183–196, 513–536, and 46 (1979), 725–731.

    Article  MathSciNet  MATH  Google Scholar 

18. R. G. Newton, Noncentral potentials: The generalized Levinson theorem and the structure of the spectrum, J. Math. Phys. 18 (1977), 1348–1357.

    Article  MathSciNet  Google Scholar 

19. V. Petkov, G. St. Popov, Asymptotic behavior of the scattering phase for non-trapping obstacles, Ann. Inst. Fourier Grenoble 32 (1982), 111–149.

    Article  MathSciNet  MATH  Google Scholar 

20. G. St. Popov, Asymptotic behavior of the scattering phase for the Schrödinger operator, preprint.

    Google Scholar 

21. D. Robert, Asymptotique de la phase de diffusion à haute énergie pour des perturbations du Laplacien, Sem. E.D.P. Ecole Polytechnique 1988–1989, Exposé no. XVII.

    Google Scholar 

22. D. Robert, Asymptotique à grande énergie de la phase de diffusion pour un potentiel, preprint 1989.

    Google Scholar 

23. D. Robert, H. Tamura, Semi-classical asymptotics for local spectral densities and time delay problems in scattering processes, J. Funct. Anal. 80 (1988), 124–147.

    Article  MathSciNet  MATH  Google Scholar 

24. B. Simon, Trace ideals and their applications, London Mathematical Society Lecture Notes Series 35, Cambridge University Press, Cambridge 1979.

    MATH  Google Scholar 

Download references