Complex transformation method and resonances in one-body quantum systems

 Access to full text

 Full (PDF)

1. [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. Zbl0219.47011MR345551
2. [BB1] D. Babbitt and E. Balslev, A characterization of dilation-analytic potentials and vectors, J. Funct. Anal., t. 18, 1975, p. 1-14. Zbl0304.47009MR384008
3. [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. MR413860
4. [B] E. Balslev, Local spectral deformation techniques for Schrödinger operators, Mittag-Leffler preprint, 1982. MR756770
5. [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. Zbl0219.47005MR345552
6. [CL] E.A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, 1955. Zbl0064.33002MR69338
7. [C] J.M. Combes, An algebraic approach to quantum scattering, 1969, unpublished manuscript. Zbl0181.27604
8. [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. Zbl0365.47025
9. [J1] A. Jensen, Local distortion technique, resonances and poles of the S-matrix, J. Math. Anal. Appl., t. 59, 1977, p. 505-513. Zbl0361.47018MR441153
10. [J2] A. Jensen, Resonances in an abstract analytic scattering theory, Ann. Inst. H. Poincaré, t. 33, 1980, p. 209-223. Zbl0462.47010MR605196
11. [Mo] E. Mourre, Absence of singular spectrum for certain self-adjoint operators, Commun. Math. Phys., t. 78, 1981, p. 391-408. Zbl0489.47010MR603501
12. [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. 
13. [N] J. Nuttall, Analytic continuation of the off-energy-shell scattering amplitude, J. Math. Phys., t. 8, 1967, p. 873-877. 
14. [RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics, I, II, IV, Academic Press. MR751959
15. [San] Sanibel WORKSHOP on Complex Scaling, 1978, in Int. J. Quant. Chemistry, t. 14, 1978. 
16. [Sig1] I.M. Sigal, Scattering Theory for Many-Body Quantum Mechanical Systems-Rigorous Results, Springer, Lecture Notes in Mathematics N1011, 1983. Zbl0522.47006MR715786
17. [Sig2] I.M. Sigal, A generalized Weyl theorem and the Lp-spectra of Schrödinger operators, J. Oper. Theory (to appear). Zbl0582.47003MR768306
18. [Sim1] B. Simon, Quadratic form technique and the Balslev-Combes theorem, Commun. Math. Phys., t. 27, 1972, p. 1-9. Zbl0237.35025MR321456
19. [Sim2] B. Simon, Resonances and complex scaling: A rigorous overview, J. Quant. Chem., t. 14, 1978, p. 529-542. 
20. [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. 
21. [T] L. Thomas, On the spectral properties of some one-particle Schrödinger Hamiltonians, Helv. Phys. Acta, t. 45, 1972, p. 1057-1065. MR376023

1. C. Gérard, Résonances et time decay en limite semiclassique
2. W. Hunziker, Distortion analyticity and molecular resonance curves
3. S. Nakamura, Distortion analyticity for two-body Schrödinger operators