Spectral perturbation bounds for selfadjoint operators [PDF]
arXiv, 2007 We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for finite eigenvalues are obtained by using analyticity and monotonicity properties (rather than variational ...
arxiv
Some inequalities for generalized eigenvalues of perturbation problems on Hermitian matrices
Journal of Inequalities and Applications, 2018 In the paper, the authors establish some inequalities for generalized eigenvalues of perturbation problems on Hermitian matrices and modify shortcomings of some known inequalities for generalized eigenvalues in the related literature.
Yan Hong, Dongkyu Lim, Feng Qi
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Asymptotic expansion for the eigenvalues of a perturbed anharmonic oscillator [PDF]
arXiv, 2019 In this article, we study the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise H\"older continuous perturbation and investigate how the H\"older constant can affect the eigenvalues. More precisely, we derive several first terms in the asymptotic expansion for the eigenvalues.
arxiv
Threshold Effects for the Generalized Friedrichs Model with the Perturbation of Rank One
Abstract and Applied Analysis, 2012 A family Hμ(p), μ>0, p∈𝕋2 of the Friedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the two-dimensional lattice ℤ2 is considered. The existence or absence of the unique eigenvalue of the operator Hμ(p)
Saidakhmat Lakaev +2 more
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Pairs of positive solutions for resonant singular equations with the p-Laplacian
Electronic Journal of Differential Equations, 2017 We consider a nonlinear elliptic equation driven by the Dirichlet p-Laplacian with a singular term and a (p-1)-linear perturbation which is resonant at $+\infty$ with respect to the principal eigenvalue. Using variational tools, together with suitable
Nikolaos S. Papageorgiou +2 more
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Studies in Perturbation Theory. XI. Lower Bounds to Energy Eigenvalues, Ground State, and Excited States [PDF]
, 1965 Per‐Olov Löwdin
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Multiple-rank modification of symmetric eigenvalue problem
MethodsX, 2018 Rank-1 modifications applied k-times (k > 1) often are performed to achieve a rank-k modification. We propose a rank- k modification for enhancing computational efficiency. As the first step toward a rank- k modification, an algorithm to perform a rank-2
HyungSeon Oh, Zhe Hu
doaj
A Simple Matrix Approach to Determination of the Helium Atom Energies
Jurnal Penelitian Fisika dan Aplikasinya, 2019 Calculation of He atomic energy levels using the first order perturbation theory taught in the Basic Quantum Mechanics course has led to relatively large errors.
Redi Kristian Pingak +2 more
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A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian [PDF]
arXiv, 2003 A two-dimensional Schr\"odinger operator with a constant magnetic field perturbed by a smooth compactly supported potential is considered. The spectrum of this operator consists of eigenvalues which accumulate to the Landau levels. We call the set of eigenvalues near the $n$'th Landau level an $n$'th eigenvalue cluster, and study the distribution of ...
arxiv
On nonlinear perturbations of the eigenvalues of a compact self-adjoint operator [PDF]
, 1967 Melvyn S. Berger
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