Abstract
O'Connor's approach to spatial exponential decay of eigenfunctions for multiparticle Schrödinger Hamiltonians is developed from the point of view of analytic perturbations with respect to transformation groups.
This framework allows an improvement of his results in some directions; in particular if interactions are dilation analytic, exponential fall-off is shown to hold for any bound-state wave-function corresponding to an eigenvalue distinct from thresholds; it is shown that the exponential decay rate depends on the distance from the bound-state energy to the nearest threshold. Applications include non existence of positive energy bound-states.
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O'Connor, A.: Exponential decay for the bound-state wave-functions of several particle systems. Princeton thesis, May 72 and Dublin advanced study institute Preprint 72
Bazley, N. W., Fox, D. W.: Intern. J. Quantum Chem.3, 581 (1969)
Faris, W. G.: Quadratic forms and essential self adjointness, to appear in Helv. Phys. Acta
Ahlrichs, R.: Asymptotic behavior of atomic bound state wave functions (Preprint 2, Theoretical Chemistry Group, University of Karlsruhe)
Kato, T.: Commun. Pure Appl. Math.10, 151 (1957)
Aguilar, J., Combes, J. M.: Commun. math. Phys.22, 269 (1971)
Balslev, E., Combes, J. M.: Commun. math. Phys.22, 280 (1971)
Simon, B.: Absence of positive eigenvalues in a class of multiparticle quantum systems. Marseille Preprint (73)
Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966
Combes, J. M.: Commun. math. Phys.12, 283 (1969)
Simon, B.: Commun. math. Phys.27, 1 (1972)
Simon, B.: Phys. Letters A-36, 23 (1971) and to appear in Annals of Mathematics
Balslev, E.: Math. Scand.19, 193 (1966)
Hunziker, W.: H.P.A.39, 451 (1966)
Ichinose, T.: On operators on tensor products of Banach spaces Nagoya University Preprint
Reed, M., Simon, B.: Tensor products of closed operators on Banach spaces. To appear in Journal of Functional Analysis
Kato, T.: T.A.M.S.70, 195 (1951)
Balslev, E.: Schrödinger operators with symmetries. CPT, CNRS. Marseille Preprint (1972)
von Neumann, J., Wigner, E.: Z. Phys.30, 465 (1929)
Simon, B.: Resonances inn-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory. Ann. Math. to appear
Kato, T.: Commun. Pure Appl. Math.12, 403 (1959)
Agmon, S.: Lower bounds for Schrödinger type equations. Proceeding of Tokyo International Conference on Functional Analysis and Related Topics, 1969
Agmon, S.: J. Analyse Math.23, 1 (1970)
Simon, B.: Comm. Pure Appl. Math.21, 531 (1968)
Messiah, A.: Quantum mechanics, Vol.II, 740. Amsterdam: North Holland Publishing Co. 1969
Kato, T.: J. Math. Soc. Japan5, 208 (1953)
Kato, T.: Commun. Pure Appl. Math.9, 479 (1956)
Yosida, K.: Functional analysis 424. Berlin-Heidelberg-New York: Springer 1968
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Combes, J.M., Thomas, L. Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators. Commun.Math. Phys. 34, 251–270 (1973). https://doi.org/10.1007/BF01646473
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DOI: https://doi.org/10.1007/BF01646473