title: A Regularized Asymptotic Solution of the Cauchy Problem for the Nonhomogeneous Schroedinger Equation in the Quasiclassical Approximation in the Presence of a "strong" Turning Point of the Limit Operator
metadata.name: dc.contributor.author
metadata.value: Eliseev, Alexander Georgievich
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kirichenko, Pavel Vladimirovich
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-04-11T10:12:22Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-04-11T10:12:22Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-03
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu35.2023.107
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/41280
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article is devoted to the development of the regularization method by S.A. Lomov on singularly perturbed problems in the presence of spectral singularities of the limit operator. In particular, a regularized asymptotic solution is constructed for the singularly perturbed inhomogeneous Cauchy problem that arises in the quasiclassical approximation in the Schroedinger equation in the coordinate representation. The potential energy profile chosen in the paper leads to a singularity in the spectrum of the limit operator in the form of a <> turning point. Based on the ideas of asymptotic integration of problems with unstable spectrum, S.A. Lomov and A.G. Eliseev, it is indicated how and from what considerations regularizing functions and additional regularizing operators should be introduced, the formalism of the regularization method for the indicated type of singularity is described in detail, this algorithm is substantiated, and an asymptotic solution of any order with respect to a small parameter is constructed.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work by supported by the Russian Ministery of Education and Science
  (ProjectFSWF-2023-0012).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Differential Equations and Control Processes;Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: singularly perturbed Cauchy problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: regularization method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: turningpoint
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A Regularized Asymptotic Solution of the Cauchy Problem for the Nonhomogeneous Schroedinger Equation in the Quasiclassical Approximation in the Presence of a "strong" Turning Point of the Limit Operator
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 110-124.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/41280/1/110-124.pdf
resources.format: Adobe PDF
resources.size: 322,74 kB