The symmetry group of the harmonic oscillator and its reduction

DOI10.1063/1.525472zbMath0494.58020OpenAlexW2092229500MaRDI QIDQ3957670

Toshihiro Iwai

Publication date: 1982

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.525472

zbMATH Keywords

quantum harmonic oscillatorfour-dimensional oscillatorHamiltonian vectorfield on an infinite dimensional symplectic manifoldquantizing classical first integralsreduction of eigenspaces of the Hamiltonian operatorreduction of the four-dimensional harmonic oscillatorreduction of the symmetry groupSchrödinger procedureSO(2)-invariant subspacesymmetries of the harmonic oscillator

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Geometric quantization (53D50) Applications of group representations to physics and other areas of science (20C35)

Related Items (7)

Reduction of Poisson manifolds ⋮ On reduction of two degrees of freedom Hamiltonian systems by an S1 action, and SO(1,2) as a dynamical group ⋮ Reduction theory and the Lagrange–Routh equations ⋮ Normalization and the detection of integrability: The generalized van der Waals potential ⋮ The quantized \(\text{SU}(2)\) Kepler problem and its symmetry group for negative energies ⋮ On a bifurcation in the quantum system for an approximation to the Hénon-Heiles system ⋮ Quantization of the conformal Kepler problem and its application to the hydrogen atom

Cites Work

• Degeneracy of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-Dimensional, Isotropic, Harmonic Oscillator
• On reduction of the four-dimensional harmonic oscillator
• Quantization of the conformal Kepler problem and its application to the hydrogen atom

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