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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
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[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
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