×

zbMATH — the first resource for mathematics

Integrable systems with Delta-potential. (English) Zbl 0517.35026

MSC:
35J10 Schrödinger operator, Schrödinger equation
35P99 Spectral theory and eigenvalue problems for partial differential equations
35Q99 Partial differential equations of mathematical physics and other areas of application
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines , Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968. · Zbl 0186.33001
[2] C. T. Benson and L. C. Grove, Finite reflection groups , Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1971. · Zbl 0579.20045
[3] F. A. Berezin, G. P. Pohil, and V. M. Finkelberg, The Schrödinger equation for a system of one-dimensional particles with point interaction , Vestnik Moskov. Univ. Ser. I Mat. Meh. 1964 (1964), no. 1, 21-28.
[4] J. B. McGuire, Study of exactly soluble one-dimensional \(N\)-body problems , J. Mathematical Phys. 5 (1964), 622-636. · Zbl 0131.43804 · doi:10.1063/1.1704156
[5] C. N. Yang, Some exact results for the many-body problem in one dimension with repulsive delta-function interaction , Phys. Rev. Lett. 19 (1967), 1312-1315. · Zbl 0152.46301 · doi:10.1103/PhysRevLett.19.1312
[6] É. Brézin and J. Zinn-Justin, Un problème à \(N\) corps soluble , C. R. Acad. Sci. Paris Sér. A-B 263 (1966), B670-B673.
[7] E. H. Lieb and W. Liniger, Exact analysis of an interacting Bose gas. I. The general solution and the ground state , Phys. Rev. (2) 130 (1963), 1605-1616. · Zbl 0138.23001 · doi:10.1103/PhysRev.130.1605
[8] Zakharov and Manakov, On the complete integrability of a nonlinear Schrödinger equation , Teor. i Mat. Fiz. 19 (1974), 332-343, (in Russian). · Zbl 0293.35025
[9] H. Bethe, Zur Theorie der Metalle, I. Eigenwerte und Eigenfunktionen der Atomkette , Zeit. Phys. 71 (1931), 205-226. · Zbl 0002.37205
[10] M. Gaudin, Boundary energy of a Base gas in one dimension , Phys. Rev. A 4 (1971), 386-394.
[11] E. Gutkin and B. Sutherland, Completely integrable systems and groups generated by reflections , Proc. Nat. Acad. Sci. U.S.A. 76 (1979), no. 12, 6057-6059. JSTOR: · Zbl 0428.35074 · doi:10.1073/pnas.76.12.6057 · links.jstor.org
[12] R. Steinberg, Differential equations invariant under finite reflection groups , Trans. Amer. Math. Soc. 112 (1964), 392-400. JSTOR: · Zbl 0196.39202 · doi:10.2307/1994152 · links.jstor.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.