# zbMATH — the first resource for mathematics

Constructive scattering theory. (English. Russian original) Zbl 1387.81362
Theor. Math. Phys. 193, No. 1, 1420-1428 (2017); translation from Teor. Mat. Fiz. 193, No. 1, 15-24 (2017).
Summary: We consider a problem of factoring the scattering matrix for Schrödinger equation on the real axis. We find the elementary factorization blocks in both the finite and infinite cases and establish a relation to the matrix conjugation problem. We indicate a general scheme for constructing a large class of scattering matrices admitting a quasirational factorization.
##### MSC:
 81U05 $$2$$-body potential quantum scattering theory
Full Text:
##### References:
 [1] Shabat, A. B., Difference Schrödinger equation and quasisymmetric polynomials, Theor. Math. Phys., 184, 1067-1077, (2015) · Zbl 1329.81176 [2] Shabat, A. B., Scattering theory for delta-type potentials, Theor. Math. Phys., 183, 540-552, (2015) · Zbl 1317.37086 [3] Shabat, A. B., Inverse spectral problem for delta potentials, JETP Lett., 102, 620-623, (2015) [4] P. Koosis, The Logarithmic Integral: I (Cambridge Stud. Adv. Math., Vol. 12), Cambridge Univ. Press, Cambridge (1997). · Zbl 0931.30001 [5] Bargman, V., Remarks on the determination of a central field of force from the elastic scattering phase shifts, Phys. Rev., 75, 301-303, (1949) · Zbl 0032.09405 [6] Shabat, A. B., Rational interpolation and solitons, Theor. Math. Phys., 179, 637-648, (2014) · Zbl 1329.34041 [7] Badakhov, M. S.h.; Shabat, A. B., Darboux transformations in the inverse scattering problem, Ufa Math. Journal, 8, 42-51, (2016) [8] Kulaev, R. C.h.; Shabat, A. B., Inverse scattering problem for finite potentials in the space of Borel measures [in russian], (2016) [9] Shabat, A. B., Functional Cantor equation, Theor. Math. Phys., 189, 1712-1717, (2016) · Zbl 1358.81155 [10] Shabat, A. B., Inverse-scattering problem for a system of differential equations, Funct. Anal. Appl., 9, 244-247, (1975) · Zbl 0352.34020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.