Reconstruction of Maslov’s Complex Germ in the Cauchy Problem for the Schrödinger Equation with a Delta Potential Localized on a Hypersurface

The semiclassical asymptotics of the solution of the Cauchy problem for the Schrödinger equation with a delta potential localized on a surface of codimension 1 is described. The Schrödinger operator with a delta potential is defined using extension theory and specified by boundary conditions on this...

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Bibliographic Details
Published inRussian journal of mathematical physics Vol. 31; no. 3; pp. 526 - 543
Main Authors Shafarevich, A.I., Shchegortsova, O.A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.09.2024
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Boundary conditions
Cauchy problems
Hyperspaces
Initial conditions
Mathematical and Computational Physics
Operators (mathematics)
Physics
Physics and Astronomy
Schrodinger equation
Theoretical
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Summary:The semiclassical asymptotics of the solution of the Cauchy problem for the Schrödinger equation with a delta potential localized on a surface of codimension 1 is described. The Schrödinger operator with a delta potential is defined using extension theory and specified by boundary conditions on this surface. The initial conditions are chosen in the form of a narrow peak, which is a Gaussian packet, localized in a small neighborhood of a surface of arbitrary dimension, and oscillating rapidly along it. The Maslov complex germ method is used to construct the asymptotics. The reflection of an isotropic manifold with a complex germ interacting with the delta potential is described. DOI 10.1134/S1061920824030142
ISSN:1061-9208
1555-6638
DOI:10.1134/S1061920824030142