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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 69 Issue: 1

Asymptotic behaviour of resonance eigenvalues of the Schrödinger operator with a matrix potential

Setenay Akduman(IZMIR DEMOCRACY UNIVERSITY)0000-0003-2492-3734
Sedef Karakılıç(DOKUZ EYLUL UNIVERSITY)0000-0002-0407-0271
Didem Coşkan(DOKUZ EYLUL UNIVERSITY)0000-0003-2358-198X
Pages
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Publication Date
2020-06-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We will discuss the asymptotic behaviour of the eigenvalues of a Schrödinger operator with a matrix potential defined by the Neumann boundary condition in L₂^{m}(F), where F is a d-dimensional rectangle and the potential is an m×m matrix with m≥2, d≥2 , when the eigenvalues belong to the resonance domain, roughly speaking they lie near the planes of diffraction.

📌 3 Key Takeaways

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Objective & Hypothesis:We will discuss the asymptotic behaviour of the eigenvalues of a Schrödinger operator with a matrix potential defined by the Neumann boundary condition in L₂^{m}(F), where F is a d-dimensional rectangle and the potential is an m×m matrix with m≥2, d≥2 , when the eigenvalues belong to the resonance domain, roughly speaking they lie near the planes of diffraction.
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Key Findings & Data:We will discuss the asymptotic behaviour of the eigenvalues of a Schrödinger operator with a matrix potential defined by the Neumann boundary condition in L₂^{m}(F), where F is a d-dimensional rectangle and the potential is an m×m matrix with m≥2, d≥2 , when the eigenvalues belong to the resonance domain, roughly speaking they lie near the planes of diffraction.
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Conclusion & Impact:We will discuss the asymptotic behaviour of the eigenvalues of a Schrödinger operator with a matrix potential defined by the Neumann boundary condition in L₂^{m}(F), where F is a d-dimensional rectangle and the potential is an m×m matrix with m≥2, d≥2 , when the eigenvalues belong to the resonance domain, roughly speaking they lie near the planes of diffraction.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Schrödinger operator · Neumann condition · Resonance eigenvalue

Abstract

We will discuss the asymptotic behaviour of the eigenvalues of a Schrödinger operator with a matrix potential defined by the Neumann boundary condition in L₂^{m}(F), where F is a d-dimensional rectangle and the potential is an m×m matrix with m≥2, d≥2 , when the eigenvalues belong to the resonance domain, roughly speaking they lie near the planes of diffraction.

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Cite This Article

Akduman, S., Karakılıç, S., Coşkan, D. (2020). Asymptotic behaviour of resonance eigenvalues of the Schrödinger operator with a matrix potential. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 1. https://doi.org/10.31801/cfsuasmas.577438

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