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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., KARAKILIÇ, 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, Cilt: 69 - Sayı: 1, 486–510. https://ajindex.com/articles/746852