General solutions of quantum mechanical equations of motion with time-dependent Hamiltonians: a Lie algebraic approach

DOI10.1016/S0034-4877(10)80007-2zbMath1194.81068arXivmath-ph/0506020MaRDI QIDQ989384

Jan Naudts, Maciej Kuna

Publication date: 20 August 2010

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0506020

zbMATH Keywords

time-dependent HamiltoniansErmakov systemmethod of the time-dependent invariant

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20)

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Cites Work

• Some physical applications of systems of differential equations admitting a superposition rule
• Recent applications of the theory of Lie systems in Ermakov systems
• General solutions of quantum mechanical equations of motion with time-dependent Hamiltonians: a Lie algebraic approach
• Dynamical symmetries and the Ermakov invariant
• Analytic approximation to the harmonic oscillator equation with a sub-period time dependent parameter
• On the generalized Maxwell-Bloch equations
• Time evolution of a time-dependent harmonic oscillator in a static magnetic field
• Time evolution of quantum systems with time-dependent Hamiltonian and the invariant Hermitian operator
• Baker - Campbell - Hausdorff relation for special unitary groups
• Baker-Campbell-Hausdorff formulas
• A class of exactly solved time-dependent quantum harmonic oscillators
• Exact Quantization Conditions. II
• Lie Algebraic Solution of Linear Differential Equations
• On Global Representations of the Solutions of Linear Differential Equations as a Product of Exponentials

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