Quadratic Hamiltonians in phase space and their eigenstates

DOI10.1063/1.524615zbMath0457.70019OpenAlexW2062075033MaRDI QIDQ3907143

Marcos Moshinsky, Pavel Winternitz

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1063/1.524615

zbMATH Keywords

symplectic Lie algebraquadratic Hamiltonianslinear canonical transformationscomplete set of commuting quadratic integrals of motion

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Schrödinger operator, Schrödinger equation (35J10) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Applications of group representations to physics and other areas of science (20C35) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15) General models, approaches, and methods in mechanics of particles and systems (70G99)

Related Items

Phase-space propagators for quantum quadratic Hamiltonians in one and two dimensions, An electron trapped in a rotating magnetic field, On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field, Collectivity and geometry. V. Spectra and shapes in the two-dimensional case, Coupled harmonic oscillator systems: An elementary algebraic decoupling approach, Collectivity and geometry. VI. Spectra and shapes in the three-dimensional case, Normal forms of elements of classical real and complex Lie and Jordan algebras, Maximal abelian subalgebras of real and complex symplectic Lie algebras, Maximal abelian subalgebras of pseudounitary Lie algebras, Symplectic formulation of relativistic quantum mechanics, Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space, Complex orthogonal and symplectic matrices depending on parameters

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