Complex transformation method and resonances in one-body quantum systems
Annales de l'I.H.P. Physique théorique, Tome 41 (1984) no. 1, p. 103-114
@article{AIHPA_1984__41_1_103_0,
author = {Sigal, I. M.},
title = {Complex transformation method and resonances in one-body quantum systems},
journal = {Annales de l'I.H.P. Physique th\'eorique},
publisher = {Gauthier-Villars},
volume = {41},
number = {1},
year = {1984},
pages = {103-114},
zbl = {0568.47008},
mrnumber = {760129},
language = {en},
url = {http://www.numdam.org/item/AIHPA_1984__41_1_103_0}
}

Sigal, I. M. Complex transformation method and resonances in one-body quantum systems. Annales de l'I.H.P. Physique théorique, Tome 41 (1984) no. 1, pp. 103-114. http://www.numdam.org/item/AIHPA_1984__41_1_103_0/

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

[BB1] D. Babbitt and E. Balslev, A characterization of dilation-analytic potentials and vectors, J. Funct. Anal., t. 18, 1975, p. 1-14. | MR 384008 | Zbl 0304.47009

[BB2] D. Babbitt and E. Balslev, Local distortion technique and unitarity of the S-matrix for the 2-body problem, J. Math. Anal. Appl., t. 54, 1976, p. 316-347. | MR 413860

[B] E. Balslev, Local spectral deformation techniques for Schrödinger operators, Mittag-Leffler preprint, 1982. | MR 756770

[BC] E. Balslev and J.M. Combes, Spectral properties of Schrödinger Hamiltonians with dilation analytic potentials, Commun. Math. Phys., t. 22, 1971, p. 280-294. | MR 345552 | Zbl 0219.47005

[CL] E.A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, 1955. | MR 69338 | Zbl 0064.33002

[C] J.M. Combes, An algebraic approach to quantum scattering, 1969, unpublished manuscript.

[Hu] W. Hunziker, The Schrödinger eigenvalue problem for N-particle systems, in The Schr&dinger Equation, W. Thrrring and P. Urban, eds., Springer-Verlag, 1977. | Zbl 0365.47025

[J1] A. Jensen, Local distortion technique, resonances and poles of the S-matrix, J. Math. Anal. Appl., t. 59, 1977, p. 505-513. | MR 441153 | Zbl 0361.47018

[J2] A. Jensen, Resonances in an abstract analytic scattering theory, Ann. Inst. H. Poincaré, t. 33, 1980, p. 209-223. | Numdam | MR 605196 | Zbl 0462.47010

[Mo] E. Mourre, Absence of singular spectrum for certain self-adjoint operators, Commun. Math. Phys., t. 78, 1981, p. 391-408. | MR 603501 | Zbl 0489.47010

[McCR] C.W. Mccurdy, Jr. and T.N. Rescigno, Extension of the method of complex basis functions to molecular resonances, Phys. Rev. Lett., t. 41, 1978, p. 1364- 1368.

[N] J. Nuttall, Analytic continuation of the off-energy-shell scattering amplitude, J. Math. Phys., t. 8, 1967, p. 873-877.

[RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics, I, II, IV, Academic Press. | MR 751959

[San] Sanibel WORKSHOP on Complex Scaling, 1978, in Int. J. Quant. Chemistry, t. 14, 1978.

[Sig1] I.M. Sigal, Scattering Theory for Many-Body Quantum Mechanical Systems-Rigorous Results, Springer, Lecture Notes in Mathematics N1011, 1983. | MR 715786 | Zbl 0522.47006

[Sig2] I.M. Sigal, A generalized Weyl theorem and the Lp-spectra of Schrödinger operators, J. Oper. Theory (to appear). | MR 768306 | Zbl 0582.47003

[Sim1] B. Simon, Quadratic form technique and the Balslev-Combes theorem, Commun. Math. Phys., t. 27, 1972, p. 1-9. | MR 321456 | Zbl 0237.35025

[Sim2] B. Simon, Resonances and complex scaling: A rigorous overview, J. Quant. Chem., t. 14, 1978, p. 529-542.

[Sim3] B. Simon, The definition of molecular resonance curves by the method of exterior complex scaling, Phys. Lett., t. 71 A, 1979, p. 211-214.

[T] L. Thomas, On the spectral properties of some one-particle Schrödinger Hamiltonians, Helv. Phys. Acta, t. 45, 1972, p. 1057-1065. | MR 376023