Abstract
We give an expository presentation of the convergence proof for asymptotic observables in N-body quantum systems. Some applications are derived. We use simplifying assumptions and add numerous remarks to stress the main ideas and techniques and to avoid technicalities. Auxiliary concepts like "k-clustered operators" and local decay of subsystems are discussed in detail.
Keywords
- Late Time
- Asymptotic Completeness
- Asymptotic Decay
- Classical Phase Space
- Schrodinger Operator
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References
V. Enss: Geometric methods in spectral and scattering theory of Schrödinger operators, in: Rigorous Atomic and Molecular Physics; G. Velo and A. S. Wightman eds., Plenum, New York 1981, pp. 1–69.
V. Enss: Asymptotic observables on scattering states, Commun. Math. Phys. 89, 245–268 (1983).
V. Enss: Quantum scattering theory for two-and three-body systems with potentials of short and long range, in: Schrödinger Operators, S. Graffi ed., Springer L N Math. 1159, Berlin 1985, p. 39–176.
V. Enss: Separation of subsystems and clustered operators for multiparticle quantum systems, preprint Nr. 213, Mathematics, Freie Universität Berlin.
Observables and asymptotic phase space localization of N-body quantum scattering states, in preparation.
R. Froese and I. Herbst: Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators, Commun. Math. Phys. 87, 429–447 (1982).
PL. Muthuramlingam and K. B. Sinha: Asymptotic completeness in long range scattering II, Ann. scient. Ec. Norm. Sup. 18, 57–87 (1985).
P. A. Perry, I. M. Sigal, and B. Simon: Spectral analysis of N-body Schrödinger operators, Ann. Math. 114, 519–567 (1981).
M. Reed, B. Simon: Methods of Modern Mathematical Physics, III. Scattering Theory, Academic Press, Now York 1979.
K. B. Sinha and PL. Muthuramalingam: Asymptotic evolution of certain observables and completeness in Coulomb scattering I, J. Func. Anal. 55, 323–343 (1984).
B. Thaller and V. Enss: Asymptotic observables and Coulomb scattering for the Dirac equation, preprint Nr. 198, Mathematik, Freie Universität Berlin; to appear in Ann. Inst. H. Poincaré Sec. A.
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© 1986 Springer-Verlag
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Enss, V. (1986). Introduction to asymptotic observables for multiparticle quantum scattering. In: Balslev, E. (eds) Schrödinger Operators, Aarhus 1985. Lecture Notes in Mathematics, vol 1218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073044
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DOI: https://doi.org/10.1007/BFb0073044
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