Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators

DOI10.1134/S0001434612090258zbMath1260.81089OpenAlexW1999924737MaRDI QIDQ1929794

A. V. Pereskokov

Publication date: 9 January 2013

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434612090258

zbMATH Keywords

WKB approximationturning pointresonancespectral clustercoherent transformoperator averaging method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (3)

Semiclassical asymptotics of the spectrum near the lower boundary of spectral clusters for a Hartree-type operator ⋮ Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters ⋮ Asymptotics of the spectrum of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters

Cites Work

• Algebra with polynomial commutation relations for the Zeeman-Stark effect in the hydrogen atom
• Algebra with polynomial commutation relations for the Zeeman effect in the Coulomb-Dirac field
• Algebra with quadratic commutation relations for an axially perturbed Coulomb-Dirac field
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Representation of exact and semiclassical eigenfunctions via coherent states. The hydrogen atom in a magnetic field
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