Distribution of primes of special kind in arithmetic progressions

Shubin, Andrei

doi:10.53815/20726759_2020_12_4_97

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2024

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“…The results of the paper are applicable in electrodynamics of continuous media [34][35][36][37], in sound wave propagation theory [38][39][40], in describing the passage of electrons through heterostructures [46][47][48][49][50], in quantum chemistry [51], in hydrodynamics and plasma physics [52], etc. In particular, the issue of proving unitarity of the S-matrix in open channels arises in describing photon scattering by metamaterials with a large spatial dispersion.…”

Section: Discussionmentioning

confidence: 99%

Multichannel scattering for the Schrödinger equation on a line with different thresholds at both infinities

Kazinski,

Korolev

2024

Proc. R. Soc. A.

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The multichannel scattering problem for the stationary Schrödinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions and of the transition matrix relating the Jost solutions as functions of the spectral parameter is described. Unitarity of the scattering matrix is proved in the general case when some of the scattering channels can be closed and the thresholds can be different at left and right infinities on the line. The symmetry relations of the S -matrix are established. The condition determining the bound states is obtained. The asymptotics of the Jost functions and of the transition matrix are derived for a large spectral parameter.

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