Algebra with polynomial commutation relations for the Zeeman-Stark effect in the hydrogen atom

DOI10.1007/s11232-005-0035-8zbMath1178.81297OpenAlexW2065103623MaRDI QIDQ844267

E. M. Novikova, Mikhail V. Karasev

Publication date: 18 January 2010

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-005-0035-8

zbMATH Keywords

integrable systemscoherent statesnonlinear commutation relationsresonance asymptotic behavior of spectrum

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie (super)algebras to physics, etc. (17B81) Atomic physics (81V45)

Related Items (9)

Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators ⋮ 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 ⋮ Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters ⋮ Algebra of symmetries of three-frequency hyperbolic resonance ⋮ Asymptotics of the spectrum of the hydrogen atom in a magnetic 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 ⋮ An application of Nekhoroshev theory to the study of the perturbed hydrogen atom

Cites Work

• Unnamed Item
• 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
• Coherent transformations and irreducible representations corresponding to complex structures on a cylinder and a torus.
• Representation of exact and semiclassical eigenfunctions via coherent states. The hydrogen atom in a magnetic field

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