Abstract
In this paper we develop the geometric methods in the spectral theory of many-body Schrödinger operators. We give different simplified proofs of many of the basic results of the theory. We prove that there are no very negative ions in Quantum Mechanics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Agmon, S.: Jerusalem, preprint 1980
Antonets, M.A., Zhislin, G.M., Shereshevskii, J.A.: Theor. Math. Phys.16, 800–808 (1972)
Bazley, N.W.: Proc. Natl. Acad. Sci. USA45, 850–853 (1959)
Bazley, N.W.: Phys. Rev.120, 144–149 (1960)
Bazley, N.W., Fox, D.W.: Phys. Rev.124, 483–492 (1961)
Bazley, N.W., Fox, D.W.: J. Res. Nat. Bur. Standards, Sect, B65, 105–111 (1961)
Combes, J.M.: In: Rigorous atomic and molecular physics. Velo, G., Wightman, A.S., (eds.) New York: Plenum 1981
Carmona, R., Simon, B.: Commun. Math. Phys.80, 59–98 (1981)
Combes, J.M., Thomas, L.: Commun. Math. Phys.34, 251–270 (1973)
Deift, P., Hunziker, W., Simon, B., Vock, E.: Commun. Math. Phys.64, 1–34 (1978)
Enss, V.: Commun. Math. Phys.52, 233–238 (1977)
Gould, S.H.: Variational methods for eigenvalue problems. Toronto: Univ. of Toronto Press, 1966
Hill, R.N.: J. Math. Phys.18, 2316–2330 (1977)
Hunziker, W.: Helv. Phys. Acta39, 451–462 (1966)
Hoffmann-Ostenhof, M., Hoffman-Ostenhof, T., Ahlrichs, R., Morgan III, J.: Mathematical problems in theoretical physics. In: Lecture Notes in Physics Vol.116. Berlin, Heidelberg, New York: 1980, 62–67
Ismagilov, R.: Sov. Math. Dokl.2, 1137–1140 (1961)
Kato, T.: (unpublished)
Klaus, M., Simon, B.: Commun. Math. Phys.78, 153–168 (1980)
Landau, L.D., Lifshitz, E.M.: Quantum mechanics. London, New York: Pergamon Press 1977
Lieb, E.H.: Rev. Mod. Phys.48, 553–569 (1976)
Morgan III, J.: J. Operat. Theor.1, 109–115 (1979)
Morgan III, J., Simon, B.: Int. J. Quant. Chem.17, 1143–1166 (1980)
O'Connor, T.: Commun. Math. Phys.32, 319–340 (1973)
Ruskai, M.B.: Commun. Math. Phys.82, 457–469 (1982)
Reed, M., Simon, B.: Methods of modern mathematical physics. New York: Academic Press 1972
Reed, M., Simon, B.: Methods of modern mathematical physics, II. New York: Academic Press 1975
Reed, M., Simon, B.: Method of modern mathematical physics, IV. New York: Academic Press 1978
Sigal, I.M.: Commun. Math. Phys.48, 137–154 (1976)
Sigal, I.M.: Duke Math. J., (submitted)
Sigal, I.M.: Proceedings of the VIth International Conference on Mathematical Physics (W. Berlin, August 11–20, 1981). In: Lecture Notes in Physics Berlin, Heidelberg, New York: Springer 1981
Sigalov, A.G., Sigal, I.M.: Theor. Math. Phys.5, 990–1005 (1970)
Simon, B.: Commun. Math. Phys.55, 259–274 (1977)
Simon, B.: Quantum mechanics for Hamiltonians defined as quadratic forms, Princeton, N.J.: Princeton Univ. Press 1970
Uchiyama, J.: Publ. Res. Inst. Math. Sci., Kyoto Univ. A,5, 51–63 (1969)
van Winter, C.: Danske V.d. Selsk. Mat.-Fys. Skr.2, 1–60; 1–94 (1964–1965)
Weinstein, A., Stanger, W.: Methods of intermediate problems for eigenvalues. New York: Academic Press 1972
Weinberger, H.F.: Variational methods for eigenvalue approximation, SIAM, Philadelphia, 1974
Yafaev, D.R.: Math. USSR, Izv.10, 861–896 (1976)
Yafaev, D.R.: Theor. Math. Phys.27, 328–343 (1977)
Zhislin, G.M.: Tr. Mosk. Mat. Obs.9, 81–128 (1960) (in Russian)
Zhislin, G.M.: Theor. Math. Phys.7, 571–578 (1971)
Zhislin, G.M.: Theor. Math. Phys.21, 971–980 (1974)
Zhislin, G.M.: Usp. Mat. N.16, 149–152 (1961) (in Russian)
Zhislin, G.M., Vugalter, S.A.: Theor. Math. Phys.32, 602–614 (1977)
Author information
Authors and Affiliations
Additional information
Communicated by B. Simon
Partially supported by USNSF Grant MCS-78-01885
Charles H. Revson Senior Scientist
Rights and permissions
About this article
Cite this article
Sigal, I.M. Geometric methods in the quantum many-body problem. Nonexistence of very negative ions. Commun.Math. Phys. 85, 309–324 (1982). https://doi.org/10.1007/BF01254462
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01254462