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Bounds on the number of eigenvalues of the Schrödinger operator. (English) Zbl 0373.35050


MSC:

35P15 Estimates of eigenvalues in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
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[1] Lieb, E.H., Thirring, W.E.: Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to SOBOLEV Inequalities. In: Studies in mathematical physics, p. 269 (eds. E.H. Lieb, B. Simon, A.S. Wightman). Princeton: Princeton University Press (1976) · Zbl 0342.35044
[2] Lieb, E.H., Thirring, W.E.: Phys. Rev. Letters35, 687 (1975)
[3] For reviews see: Simon, B.: In Ref. [1], p. 306
[4] Martin, A.: CERN Preprint TH. 2294 (1977), to appear in the Proceedings of the Winter School of the Indian National Science Academy (1977)
[5] Martin, A.: A bound on the total number of bound states in a potential. CERN Preprint TH. 2085 (unpublished) (1975)
[6] Rozenblum, G.V.: Soviet Math. Dokl.13, 245 (1972)
[7] Cwikel, M.: I.A.S. Preprint (1976)
[8] Lieb, E.H.: Bull. Am. Math. Soc.82, 751 (1976) · Zbl 0329.35018
[9] Glaser, V., Martin, A., Grosse, H., Thirring, W.: A family of optimal conditions for the absence of bound states in a potential. In Ref. [1], Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to SOBOLEV Inequalities. In: p. 169 · Zbl 0332.31004
[10] Courant, R., Hilbert, D.: Methods of mathematical physics. New York: Interscience Publishers 1953 · Zbl 0051.28802
[11] Sêto, N.: Publ. RIMS, Kyoto University9, 429 (1974)
[12] Birman, M.S.: Am. Math. Soc. Transl., Ser. 2,53, 23 (1966); Schwinger, J.: Proc. Nat. Acad. Sci.47, 122 (1961)
[13] Zakharov, V.E., Faddeev, L.D.: Funct. Anal. Appl.5, 280 (1971) · Zbl 0257.35074
[14] Fubini, S.: Nuovo Cimento34A, 521 (1976)
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