Schroedinger Operators. The Quantum Mechanical Many-Body by Erik Balslev

By Erik Balslev

In those lawsuits simple questions relating to n-body Schr|dinger operators are handled, equivalent to asymptotic completeness of structures with long-range potentials (including Coulomb), a brand new evidence of completeness for short-range potentials, strength asymptotics of huge Coulomb systems,asymptotic neutrality of polyatomic molecules. different contributions deal withdifferent forms of difficulties, corresponding to quantum balance, Schr|dinger operators on a torus and KAM idea, semiclassical concept, time hold up, radiation stipulations, magnetic Stark resonances, random Schr|dinger operators and stochastic spectral research. the quantity provides the implications in such element that it can good function simple literature for seminar paintings.

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Baxter (1972) Ann. Phys. 70, 323–337. M. L¨ uscher (1976) Nucl. Phys. B117, 475–492. The definition of t(k)(u) is taken from (Kulish, Sklyanin, 1982a), see above. For the master symmetries for quantum integrable chains see M. G. Tetelman (1982) Sov. Phys. JETP 55(2), 306–310. E. Barouch, B. Fuchssteiner (1985) Stud. Appl. Math. 73, 221–237. H. Araki (1990) Commun. Math. Phys. 132, 155–176. The boost operator B was shown recently to have close relation to Baxter’s corner transfer matrices H. Itoyama, H.

Mod. Phys. 4, 3759–3777. For more sophisticated treatment of the Yang-Baxter equation based on the Quantum Group theory see V. G. Drinfeld (1985) Sov. Math. Dokl. 32, 254–258. V. G. Drinfeld (1988) Sov. Math. Dokl. 36, 212–216. V. G. Drinfeld (1987) Quantum Groups, in Proceedings of the International Congress of Mathematicians, Berkeley, 1986, American Mathematical Society, 798–820. L. A. Takhtajan (1989) in Nankai Lectures on Mathematical Physics, Introduction to Quantum Group and Integrable Massive Models of Quantum Field Theory, eds.

Ezawa (1987) Progr. Theor. Phys. 78, 1009–1021. Separation of variables in the quantum Goryachev-Chaplygin top (gyrostat) was obtained in I. V. Komarov (1982) Theor. & Math. Phys. 50, 265–270. I. V. Komarov, V. V. Zalipaev (1984) J. Phys. A: Math. Gen. 17, 31–49. 35 The Functional Bethe Ansatz was proposed in papers E. K. 196–233, Berlin: Springer. E. K. Sklyanin (1985b) J. Sov. Math. 31, 3417–3431. influenced deeply by the articles H. Flashka, D. W. McLaughlin (1976) Progr. Theor. Phys. 55, 438–456.

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