×

A factorization of the scattering matrix for the Schrödinger equation and for the wave equation in one dimension. (English) Zbl 0762.35075

Summary: For the one-dimensional Schrödinger equation with a potential decaying at both ends of the real axis, the scattering matrix of the potential is given explicitly in terms of the scattering matrices corresponding to the fragments of this potential. A similar result also holds for the wave equation in a nonhomogeneous, nondispersive medium, where the wave speed has the same asymptotics at both ends of the real line.

MSC:

35P25 Scattering theory for PDEs
81U20 \(S\)-matrix theory, etc. in quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Faddeev L. D., Am. Math. Soc. Transl. 2 pp 139– (1964)
[2] Faddeev L. D., Trudy Mat. Inst. Stekl. 73 pp 314– (1964)
[3] DOI: 10.1063/1.524447 · Zbl 0446.34029
[4] DOI: 10.1063/1.529650 · Zbl 0760.35032
[5] DOI: 10.1119/1.16705
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.