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Scattering and local absorption for the Schrödinger operator. (English) Zbl 0382.47004

47A40 Scattering theory of linear operators
35J10 Schrödinger operator, Schrödinger equation
35P25 Scattering theory for PDEs
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
Full Text: DOI
[1] Agmon, S., Spectral properties of Schrödinger operators and scattering theory, Ann. scuola. norm. sup. Pisa, 2, 151-218, (1975) · Zbl 0315.47007
[2] Amrein, W.O., Some questions in nonrelativistic quantum scattering theory, (), 97-140 · Zbl 0299.47008
[3] Amrein, W.O.; Georgescu, V., On the characterization of bound states and scattering states in quantum mechanics, Helv. phys. acta, 46, 635-658, (1973)
[4] Amrein, W.O.; Georgescu, V., Strong asymptotic completeness of wave operators for highly singular potentials, Helv. phys. acta, 47, 517-533, (1974)
[5] Baeteman, M.L.; Chadan, K., Scattering theory with highly singular oscillating potentials, Ann. inst. H. Poincaré, 24, 1-16, (1976)
[6] Belopolskii, A.L.; Birman, M.Sh., The existence of wave operators and scattering theory for pairs of spaces, Math. USSR izv., 2, 1117-1130, (1968) · Zbl 0186.20803
[7] Combescure, M.; Ginibre, J., Spectral and scattering theory for the Schrödinger operator with strongly oscillating potentials, Ann. inst. H. Poincaré, 24, 17-29, (1976) · Zbl 0336.47007
[8] Deift, P.; Simon, B., On the decoupling of finite singularities from the question of asymptotic completeness in two-body quantum systems, J. funct. anal., 23, 218-238, (1976) · Zbl 0344.47007
[9] Ikebe, T.; Kato, T., Uniqueness of self adjoint extensions of singular elliptic differential equations, Arch. rational. mech. anal., 9, 77-92, (1962) · Zbl 0103.31801
[10] Kato, T., Perturbation theory for linear operators, (1966), Springer Berlin · Zbl 0148.12601
[11] Pearson, D.B.; Whould, D.H., On existence and asymptotic completeness of the wave operators for spherically symmetric potentials, Nuovo cimento A, 14, 765-780, (1973)
[12] Pearson, D.B., Time dependent scattering theory for highly singular potentials, Helv. phys. acta, 47, 249-264, (1974)
[13] Pearson, D.B., General theory of potential scattering with absorption at local singularities, Helv. phys. acta, 48, 639-653, (1975)
[14] Pearson, D.B., A generalization of the Birman trace theorem, J. funct. anal., 28, 182-186, (1978) · Zbl 0382.47006
[15] Pearson, D.B., An example in potential scattering illustrating the breakdown of asymptotic completeness, Comm. math. phys., 40, 125-146, (1975)
[16] Reed, M.; Simon, B., ()
[17] Robinson, D.W., Scattering theory with singular potential. I. the two-body problem, Ann. inst. H. Poincaré, 21, 185-215, (1974)
[18] Ruelle, D., A remark on bound states in potential scattering theory, Nuovo cimento A, 61, 655-662, (1969)
[19] Schechter, M., Scattering theory for elliptic operators of arbitrary order, Comment. math. helv., 49, 84-113, (1974) · Zbl 0288.47012
[20] Skriganov, M.M., Spectrum of the Schrödinger operator with strongly oscillating potentials, (), 187-195, (in Russian)
[21] Wilcox, C.H., Scattering states and wave operators in the abstract theory of scattering, J. funct. anal., 12, 257-274, (1973) · Zbl 0248.47006
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