Asymptotics of the spectrum of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters

DOI10.1090/S0077-1554-2013-00205-8zbMath1270.81098MaRDI QIDQ2837780

A. V. Pereskokov

Publication date: 11 July 2013

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

WKB approximationturning pointcoherent transformationspectral clusteroperator averaging method

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Atomic physics (81V45) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Classical hypergeometric functions, ({}_2F_1) (33C05) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (4)

Asymptotics of the spectrum of the hydrogen atom in orthogonal electric and magnetic fields near the lower boundaries of spectral clusters ⋮ Semiclassical asymptotics of the spectrum of the hydrogen atom in an electromagnetic field near the upper boundaries of spectral clusters ⋮ Semiclassical asymptotics of the spectrum of the hydrogen atom in an electromagnetic field near the lower boundaries of spectral clusters ⋮ On the asymptotics of the spectrum of the hydrogen atom in orthogonal electric and magnetic fields near the upper boundaries of spectral clusters

Cites Work

• Algebra with polynomial commutation relations for the Zeeman-Stark effect in the hydrogen atom
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• Algebra with quadratic commutation relations for an axially perturbed Coulomb-Dirac field
• Noncommutative algebras, nano-structures, and quantum dynamics generated by resonances. III.
• Schrödinger operators with magnetic fields. III: Atoms in homogeneous magnetic 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
• Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators
• Asymptotic and geometric quantization
• The Zeeman effect for the 'anistropic hydrogen atom' in the complex WKB approximation: I. Quantization of closed orbits for the Pauli operator with spin-orbit interaction
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