Unitary transformation approach to the exact solution for a class of time-dependent nonlinear Hamiltonian systems

DOI10.1063/1.532341zbMath0908.35110OpenAlexW2000169167MaRDI QIDQ4212624

Mustapha Maamache

Publication date: 6 October 1998

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

Full work available at URL: https://doi.org/10.1063/1.532341

zbMATH Keywords

exact solutionnonlinear Hamiltonian systemsnonadiabatic Berry's phaseunitary transformations on the time-dependent Schrödinger equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (5)

Perturbed Landau system and non-adiabatic Berry's phase in two dimensions ⋮ Wave Functions for Time-Dependent Dirac Equation under GUP ⋮ Nonautonomous Hamiltonian quantum systems, operator equations, and representations of the Bender-Dunne Weyl-ordered basis under time-dependent canonical transformations ⋮ Quasi-coherent states for damped and forced harmonic oscillator ⋮ Quasi-coherent states for a photon in time varying dielectric media

Cites Work

• Invariant-angle coherent states for the singular oscillator and geometrical phases and angles
• The exact solution for the generalized time-dependent harmonic oscillator and its adiabatic limit
• Quantal phase factors accompanying adiabatic changes
• An application of Ray–Reid invariants
• Gauge transformation approach to the exact solution of a generalized harmonic oscillator
• Class of Exact Invariants for Classical and Quantum Time-Dependent Harmonic Oscillators

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