Abstract
The spatial decay properties of the wave functions of multiparticle systems are investigated. The particles interact through pair potentials in the classR+L ∞ɛ . The bound states lie below the bottom of the continuous spectrum of the system. Exponential decay, in anL 2 sense, is proven for these wave functions. The result is the best possible one which will cover every potential in this class.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ahlrichs, R.: Preprint 1972, Institut für Physikalische Chemie der Universität Karlsruhe
Bochner, S., Martin, W. T.: Several complex variables. Princeton: University Press 1948
Combes, J. M.: Nuovo Cimento64A, 111 (1969)
Federbush, P. G.: Phys. Rev.148, 1551 (1966)
Hepp, K.: Helv. Phys. Acta42, 425 (1969)
Hunziker, W. Phys. Rev.135, B 800 (1964)
Hunziker, W.: J. Math. Phys.7, 300 (1966)
Kato, T.: Commun. Pure and Appl. Math.10, 151 (1957)
Newton, R. G.: Phys. Rev.153, 1502 (1967)
Paley, R. E. A. C., Wiener, N.: Fourier transforms in the complex plane. Amer. Math. Soc. Colloq. Publn. 19 (1934)
Reed, M., Simon, B.: Methods of Modern Mathematical Physics (Vol. I). New York: Academic Press 1972
Alfaro, V. de, Regge, T.: Potential scattering. Amsterdam: North Holland 1965
Schnoll, I. E.: Mathematicheskii Sbornik42, 84, 3 (1951)
Glazman, I. M.: Direct methods in the qualitative spectral analysis of singular differential operators. Israeli Program for Scientific Translations, Jerusalem 1965
Simon, B.: Quantum mechanics for hamiltonians defined as quadratic forms, Princeton University Press 1971
Slaggie, E. L., Wichmann, E. H.: J. Math. Phys.3, 946 (1962)
Titchmarsh, E. C.: Introduction to the theory of the Fourier integral. Oxford: Oxford University Press 1937
van Winter, C.: Mat. Fys. Skr. Dan. Vid. Selsk.1, 8 (1964);1, 10 (1965)
Weinberg, S.: Phys. Rev.133, 232 (1964)
Nelson, E.: Annal of Math.70, 572 (1959)
Schminke, U.-W.: Math. Z.11, 267 (1969)
Combes, J. M.: Commun. math. Phys.12, 283 (1969)
van Winter, C., Brascamp, H. J.: Commun. math. Phys.11, 19 (1968)
Nelson, E.: J. Math. Phys.5, 332 (1964)
Balslev, E.: Math. Scand.19, 193 (1966)
Simon, B.: IHES preprint, December 1972. Pointwise Bounds on Eigenfunctions and Wave Packets inN-Body Quantum Systems
Thomas, L.: Preprint, Université de Genève, Départment de Physique Théorique Combes, J. M.: Preprint, Department of Mathematics, Centre Universitaire de Toulon
Author information
Authors and Affiliations
Additional information
Based on a thesis submitted to Princeton University in partial fulfillment of the degree of Doctor of Philosophy.
Rights and permissions
About this article
Cite this article
O'Connor, A.J. Exponential decay of bound state wave functions. Commun.Math. Phys. 32, 319–340 (1973). https://doi.org/10.1007/BF01645613
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01645613