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References
Agmon, S.: Scattering theory for long-range potentials, Lectures on the Salt lake City Conference (1978)
Amrein, W.O., Jauch, M., Sinha, K.B.: Scattering theory in quantum mechanics, Benjamin Reading, Mass.: (1977)
Cordes, H.: On compactness of commutators of multiplications and convolutions, and boundedness of pseudo-differential operators. J. Funct. Anal.18, 115–131 (1975)
Cycon, H.L.: An upper bound for the local time-decay of scattering solutions for the Schrödinger equation with Coulomb potential, in Ann. de l'Inst. H. Poincaré, Phys. Théorique29, 385–392 (1983)
Cycon, H.L.: Absence of singular continuous spectrum of Schrödinger operators with longrange potentials (a new proof), Proc. Roy. Soc. Edinburgh94A, 61–69 (1983)
Enss, V.: Propagation properties of quantum scattering states, Rep. No 10, Inst. Mittag-Leffler, to appear in J. Funct. Anal. (1982)
Jensen, A.: Spectral properties of Schrödinger operators and time-decay of the wave functions; results inL 2(ℝm),m≧5; Duke Math. J.47, 1, 57–80 (1980)
Jensen, A., Kato, T.: Spectral properties of Schrödinger operators and time decay of the wave functions, Duke Math. J. Vol.46, 3, 583–611 (1979)
Jensen, A., Mourre, E., Perry, P.: Multiple commutator estimates and resolvent smoothness in quantum scattering theory, to appear in Ann. de L'Institut H. Poincavé (1983)
Kato, T.: Perturbation theory for linear operators; Berlin, Heidelberg, New York: Springer 1966
Kitada, H.: Time-decay of the high energy part of the solution for a Schrödinger equation, to appear in J. Fac. Sci., Univ. of Tokyo, Sec. I A (1983)
Klein, M.: Streutheorie für langreichweitige Potentiale, Appendix; Diplomarbeit TU Berlin (1983)
Mourre, E.: Link between the geometrical and the spectral transformation approaches in scattering theory. Comm. Math. Phys.68, 91–94 (1979)
Mourre, E.: Absence of singular continuous spectrum for certain self-adjoint operators. Comm. Math. Phys.78, 391–408 (1981)
Murata, M.: Asymptotic expansion in time for solutions of Schrödinger-type equations. J. Funct. Anal.49, 10–56 (1982)
Perry, P.A.: Propagation of states in dilation analytic potentials and asymptotic completeness, Comm. Math. Phys.81, 243–259 (1981)
Perry, P.A., Signal, I.M., Simon, B.: Spectral analysis ofN-body Schrödinger operators, Ann. Math.114, 519–567 (1981)
Rauch, J.: Local decay of scattering solution to Schrödinger equation, Comm. Math. Phys.61, 149–168 (1981)
Reed, M., Simon, B.: Methods of Modern Mathematical physics IV, New York: Acad. Press 1978
Reed, M., Simon, B.: Methods of Modern Mathematical Physics II, New York: Academic Press 1975
Sigal, I.M., Complex transformation method and resonances in one body quantum systems. Preprint, Weizmann Institute (1983)
Taylor, M.E.: Pseudodifferential operators. Princeton. Princeton University Press 1981
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Cycon, H.L., Perry, P.A. Local time-decay of high energy scattering states for the Schrödinger equation. Math Z 188, 125–142 (1984). https://doi.org/10.1007/BF01163881
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DOI: https://doi.org/10.1007/BF01163881