Analytic scattering theory of quantum mechanical three-body systems
Balslev, Erik
Annales de l'I.H.P. Physique théorique, Tome 33 (1980), p. 125-160 / Harvested from Numdam
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@article{AIHPA_1980__32_2_125_0,
     author = {Balslev, Erik},
     title = {Analytic scattering theory of quantum mechanical three-body systems},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {33},
     year = {1980},
     pages = {125-160},
     mrnumber = {580324},
     zbl = {0428.47003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1980__32_2_125_0}
}

Balslev, Erik. Analytic scattering theory of quantum mechanical three-body systems. Annales de l'I.H.P. Physique théorique, Tome 33 (1980) pp. 125-160. http://gdmltest.u-ga.fr/item/AIHPA_1980__32_2_125_0/

[1] S. Agmon, Lower bounds for solutions of Schrödinger equations, J. d'Anal. Math., 23, 1, 1970, p. 1-25. | MR 276624 | Zbl 0211.40703

[2] S. Agmon, Spectral properties of Schrödinger operators and scattering theory, Ann. d. Scuola Norm. sup. de Pisa, Cl. d. Scienze ser. IV, vol. II, 2, 1975, p. 151-218. | Numdam | MR 397194 | Zbl 0315.47007

[3] F. Aguilar and J.M. Combes, On a class of analytic perturbations of one-body Schrödinger operators, Comm. Math. Phys., 22, 1971, p. 269-279. | MR 345551 | Zbl 0219.47011

[4] D. Babbitt and E. Balslev, A characterization of dilation-analytic potentials and vectors, J. Funct. Anal., vol. 18, no. 1, 1975, p. 1-14. | MR 384008 | Zbl 0304.47009

[5] E. Balslev and J.M. Combes, Spectral properties of many-body Schrödinger operators with dilation-analytic interactions, Comm. Math. Phys., t. 22, 1971, p. 280-299. | MR 345552 | Zbl 0219.47005

[6] E. Balslev, Spectral theory of Schrödinger operators of many-body systems with permutation and rotation symmetries, Ann. Phys., t. 73, 1972, p. 49-107 ; Schrödinger operators with symmetries I-II, Reports on Mathematical Physics, t. 5, 1974, p. 219-280 et p. 393-413. | MR 332037

[7] E. Balslev, Decomposition of many-body Schrödinger operators, Comm. Math. Phys., t. 52, 1977, p. 127-146. | MR 438950 | Zbl 0352.35038

[8] E. Balslev, Analytic scattering theory of 2-body Schrödinger operators, J. Funct. Anal., t. 29, 3, 1978, p. 375-396. | MR 512251 | Zbl 0392.47003

[9] E. Balslev, Scattering theory of dilated 3-body Schrödinger operators, J. Quantum Chem., t. 14, 1978, p. 361-370.

[10] E. Balslev, Analytic scattering theory of quantum mechanical three-body systems, Aarhus University Preprint, no. 26, 1979. | Zbl 0405.47008

[11] E. Balslev, Analytic scattering theory for many-body systems below the smallest three-body threshold, Aarhus University Preprint, 1979. to appear, Comm. Math. Phys. | MR 589431 | Zbl 0436.35068

[12] J.M. Combes and L.E. Thomas, Asymptotic behaviour of eigenfunction for multiparticle Schrödinger operators, Comm. Math. Phys., t. 34, 1973, p. 251- 270. | MR 391792 | Zbl 0271.35062

[13] L.D. Faddeev, Mathematical aspects of the three-body problem in quantum scattering theory, Israel program for scientific translations, Jerusalem, 1975. | MR 221828

[14] J. Ginibre and M. Moulin, Hilbert space approach to the quantum-mechanical three-body problem, Ann. Inst. Poincaré, vol. XXI, no. 2, 1974, p. 97-145. | Numdam | MR 368656 | Zbl 0311.47003

[15] G.A. Hagedorn, Asymptotic completeness for a class of four particle Schrödinger operators, Bull. Ann Math. Soc., t. 84, 1, 1978, p. 155-156. | MR 496030 | Zbl 0389.47006

[16] G.A. Hagedorn, A link between scattering resonances and dilation analytic resonances in few body quantum mechanics, Comm. Math. Phys., t. 65, 2, 1979, p. 181-188. | MR 528190 | Zbl 0404.47007

[17] K. Hepp, On the quantum-mechanical N-body problem, Helv. Phys. Acta, t. 42, 1969, p. 425-458. | MR 247840

[18] J.S. Howland, Abstract stationary theory of multichannel scattering, J. Funct. Anal., t. 22, 1976, p. 250-282. | MR 461175 | Zbl 0327.47004

[19] R.J. Iorio and M. O'Carroll, Asymptotic completeness for multiparticle Schrödinger operators with weak potentials, Comm. math. Phys., t. 27, 1972, p. 137- 145. | MR 314392

[20] A. Jensen, Local decay in time of solutions to Schrödinger's equation with dilation-analytic interaction, Manuscripta Math., t. 25, 1978, p. 61-77. | MR 492959 | Zbl 0397.35056

[21] T. Kako and K. Yajima, Spectral and scattering theory for a class of nons-elfadjoint operators, Sci. papers College Gen. Ed. Univ. Tokyo, t. 26, 1976, p. 73-89. | MR 500220 | Zbl 0349.47010

[22] T. Kato, Wave operators and similarity for some none-selfadjoint operators, Math. Ann., t. 162, 1966, p. 258-279. | MR 190801 | Zbl 0139.31203

[23] T. Kato, Perturbation Theory for Linear Operators, 2 nd. ed. Springer-Verlag, 1976. | MR 407617 | Zbl 0342.47009

[24] T. Kato, Two space scattering, with applications to many-body problems, J. Fac. Sci. Univ. Tokyo, Sect. IA, t. 24, 1977, p. 503-514. | MR 512674 | Zbl 0395.47007

[25] S.T. Kuroda, An abstract stationary approach to perturbation of continuous spectra and scattering theory, J. d'Analyse Math., t. 20, 1967, p. 57-117. | MR 216331 | Zbl 0153.16903

[26] S.T. Kuroda, An introduction to scattering theory, Aarhus University Lecture notes, Series 51, Feb. 1979. | MR 528757 | Zbl 0407.47003

[27] R. Lavine, Commutators and scattering theory II, A class of one body problems, Indiana Univ. Math. J., t. 21, 1972, p. 643-656. | MR 300134 | Zbl 0216.38501

[28] J.L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, vol. I, Springer-Verlag, 1972. | MR 350177 | Zbl 0223.35039

[29] E. Mourre, Applications de la méthode de Lavine au problème à trois corps, Ann. Inst. Poincaré, Sect. A, t. 26, 3, 1977, p. 219-262. | Numdam | MR 441155 | Zbl 0364.47005

[30] M. Reed and B. Simon, Methods of modern mathematical physics, IV, Academic Press, 1978. | MR 751959 | Zbl 0401.47001

[31] I.M. Sigal, Mathematical Foundations of quantum scattering theory for multiparticle systems, Mem. A. M. S., vol. 16, no. 2, 1978, p. 209. | MR 508478 | Zbl 0399.47008

[32] I.M. Sigal, On quantum mechanics of many-body systems with dilation analytic potentials, Bull. A. M. S., t. 84, 1, 1978, p. 152-154. | MR 459410 | Zbl 0399.47009

[33] S. Steinberg, Meromorphic families of compact operators, Arch. Rat. Mech. Anal., t. 31, 1968, p. 372-379. | MR 233240 | Zbl 0167.43002

[34] L.E. Thomas, Asymptotic completeness in two-and three particle quantum mechanical scattering, Ann. Phys., t. 90, 1975, p. 127-165. | MR 424082

[35] C. Van Winter, Complex dynamical variables for multiparticle systems with analytic interactions I-II, J. Math. Anal. Appl., t. 47, 1974, p. 633-670; t. 48, 1974, p. 368-399. | MR 368663 | Zbl 0321.47004

[36] C. Van Winter, Invariant subspaces of analytic multiparticle Hamiltonians, J. Math. Anal. Appl., t. 49, 1975, p. 88-123. | MR 356783 | Zbl 0296.46026

[37] C. Van Winter, Projection operators associated with analytic multiparticle Hamiltonians Notices, Am. Math. Soc., t. 25, 1978, A-320.

[38] K. Yajima, An abstract stationary approach to three-body scattering, J. Fac. Sci. Univ. Tokyo, Sect. IA, t. 25, 1978, p. 109-132. | MR 494598 | Zbl 0398.35072