Fifty years of eigenvalue perturbation theory
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Publication:3971806
DOI10.1090/S0273-0979-1991-16020-9zbMath0739.47006OpenAlexW2071731927MaRDI QIDQ3971806
Publication date: 25 June 1992
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0273-0979-1991-16020-9
anharmonic oscillatoreigenvalue perturbation theoryBerry's phaseregular perturbation theorydouble wellsautoionizing statesisoelectric atomsNewton diagram method of branching theoryZeeman and Stark effects
Applications of operator theory in the physical sciences (47N50) Perturbation theory of linear operators (47A55) Eigenvalue problems for linear operators (47A75)
Related Items (23)
Splitting of resonant and scattering frequencies under shape deformation ⋮ Approximations of strongly continuous families of unbounded self-adjoint operators ⋮ On stationary Schrödinger-Poisson equations modelling an electron gas with reduced dimension ⋮ Extrapolation of perturbation-theory expansions by self-similar approximants ⋮ Mathematical properties of a new Levin-type sequence transformation introduced by Čı́žek, Zamastil, and Skála. I. Algebraic theory ⋮ Eigenvalues and eigenfunctions for the ground state of polynomial potentials ⋮ Summation of divergent power series by means of factorial series ⋮ Asymptotic property for eigenelements of the Laplace operator in a domain with an oscillating boundary ⋮ Asymptotic analysis of spectral problems in thick junctions with the branched fractal structure ⋮ Additive self-similar approximants ⋮ The asymptotic iteration method for the eigenenergies of the anharmonic oscillator potential \(V(x)=Ax^{2\alpha} +Bx^2\) ⋮ Schrödinger operators in the twentieth century ⋮ r D oscillators with arbitrary D>0 and perturbation expansions with Sturmians ⋮ Boundary-variation solution of eigenvalue problems for elliptic operators. ⋮ Self-similar continued root approximants ⋮ Approximation of PDE eigenvalue problems involving parameter dependent matrices ⋮ Approximate analytical states of a polynomial potential: an example of symmetry restoration ⋮ The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations ⋮ Eigenvalue perturbation and generalized Krylov subspace method ⋮ Convergent Rayleigh-Schrödinger perturbation expansions for low-lying eigenstates and eigenenergies of anharmonic oscillators in intermediate basis states ⋮ THE ASYMPTOTIC ITERATION METHOD FOR THE EIGENENERGIES OF THE ASYMMETRICAL QUANTUM ANHARMONIC OSCILLATOR POTENTIALS $V(x)=\sum_{j=2}^{2\alpha}A_{j}x^{j}$ ⋮ Stark resonances: Asymptotics and distributional Borel sum ⋮ Hausdorff convergence and asymptotic estimates of the spectrum of a perturbed operator
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