Regularized Asymptotics of the Solution of a Singularly Perturbed Mixed Problem on the Semiaxis for the Schrödinger Equation with the Potential Q = X 2

Alexander Yeliseev (), Tatiana Ratnikova and Daria Shaposhnikova
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Alexander Yeliseev: National Research University Moscow Power Engineering Institute, 111250 Moscow, Russia
Tatiana Ratnikova: National Research University Moscow Power Engineering Institute, 111250 Moscow, Russia
Daria Shaposhnikova: National Research University Moscow Power Engineering Institute, 111250 Moscow, Russia

Mathematics, 2023, vol. 11, issue 20, 1-20

Abstract: In this paper, we study the solution of a singularly perturbed inhomogeneous mixed problem on the half-axis for the Schrödinger equation in the presence of a “strong” turning point for the limit operator on time interval that do not contain focal points. Based on the ideas of the regularization method for asymptotic integration of problems with an unstable spectrum, it is shown how regularizing functions should be constructed for this type of singularity. The paper describes in detail the formalism of the regularization method, justifies the algorithm, constructs an asymptotic solution of any order in a small parameter, and proves a theorem on the asymptotic convergence of the resulting series.

Keywords: singularly perturbed problem; asymptotic solution; regularization method; turning point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:20:p:4328-:d:1261737

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