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.
complété par Addendum “Complex transformation method and resonances in one-body quantum systems” 
@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},
     pages = {103--114},
     publisher = {Gauthier-Villars},
     volume = {41},
     number = {1},
     year = {1984},
     mrnumber = {760129},
     zbl = {0568.47008},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1984__41_1_103_0/}
}
TY  - JOUR
AU  - Sigal, I. M.
TI  - Complex transformation method and resonances in one-body quantum systems
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1984
SP  - 103
EP  - 114
VL  - 41
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1984__41_1_103_0/
LA  - en
ID  - AIHPA_1984__41_1_103_0
ER  - 
%0 Journal Article
%A Sigal, I. M.
%T Complex transformation method and resonances in one-body quantum systems
%J Annales de l'I.H.P. Physique théorique
%D 1984
%P 103-114
%V 41
%N 1
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1984__41_1_103_0/
%G en
%F 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 | Zbl

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

[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

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

[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 | Zbl

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

[C] J.M. Combes, An algebraic approach to quantum scattering, 1969, unpublished manuscript.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

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

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

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

[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

[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 | Zbl

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

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

[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