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By K. Osterwalder

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Extra resources for Mathematical problems in theoretical physics: proceedings of the International Conference on Mathematical Physics held in Lausanne, Switzerland, August 20-25, 1979

Sample text

It is easy to see that this potential has no bound states below the continuum for sufficiently small Z, which implies that H S has no bound states below the continuum for sufficiently small Z, and in turn that the original two electron atomic system has no bound state below -i for y = 0 and Z sufficiently small. The value of Z at which the bound state disappears is not known. The values Z = i, y = 1/2 arise for two electrons plus a positron. of bound states of this system is also not known with certainty, but The number the question could be settled via the methods used for H- if a less drastic approximation is used to handle the Hughes-Eckart term.

Acad. Sci. U. S. A. 4_~5,850-853 (1959) and Phys. Rev.

17, 46 (1976). P. LAX and R. PHILLIPS, Scattering Theory , Academic Press, New York, 1967. [27] [28] [30] [31] [33] [34 [35] [37] [38] [39] Bo] BI] [43] [44 [45] [46] P. DEIFT and B. SIMON, On the decoupling of f i n i t e singularities from the question of asymptotic completeness, J. Funct. Anal. Z3, 218 (i~76). A. JENSEN and T. KATO, Asymptotic behaviour of the scattering phase for exterior domains, Commun. E 3, 12, 1105 (1978). M. COMBESCUREand J. GINIBRE, Scattering and local absorption for the Schr~dinger operator, J.

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