On the theory of time-dependent linear canonical transformations as applied to Hamiltonians of the harmonic oscillator type

DOI10.1063/1.523447zbMath0365.70019OpenAlexW2019451569MaRDI QIDQ4140439

Publication date: 1977

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

Full work available at URL: https://doi.org/10.1063/1.523447

Mathematics Subject Classification ID

Hamilton's equations (70H05) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (19)

Exact solution of Schrödinger equation for two state problem with time dependent coupling ⋮ A necessary and sufficient condition for the stability of linear Hamiltonian systems with periodic coefficients ⋮ Exact results for the Schrödinger equation with moving localized potential ⋮ Time-dependent Schrödinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations ⋮ Reduced phase space optics for general relativity: symplectic ray bundle transfer ⋮ Second quantized scalar QED in homogeneous time-dependent electromagnetic fields ⋮ Ermakov systems, exact solution, and geometrical angles and phases ⋮ First integrals via polynomial canonical transformations ⋮ On nonlinear transformations for time-dependent polynomial Hamiltonians ⋮ Towards an invariant for the time-dependent anharmonic oscillator ⋮ Symbolic computation of approximate symmetries for ordinary differential equations ⋮ Generalisations of the LaplaceRungeLenz Vector ⋮ Quadratic Hamiltonians: The four classes of quadratic invariants, their interrelations and symmetries ⋮ The complete symmetry group of the one-dimensional time-dependent harmonic oscillator ⋮ Lie algebraic treatment of the quadratic invariants for a quantum system ⋮ Schrödinger equation with time-dependent boundary conditions ⋮ Dynamical Noether invariants for time-dependent nonlinear systems ⋮ Exact invariants for a class of time-dependent nonlinear Hamiltonian systems ⋮ Classification scheme for two-dimensional Ermakov-type systems and generalizations

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