Dynamical Invariants for Variable Quadratic Hamiltonians

Abstract

We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problems for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansionof the solution of the initial value problem is also found. A nonlinear superposition principle for the generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

21 pages, no figures; to appear in Physica Scripta

References in corpus (3)

• Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields
• Solution of the Cauchy Problem for a Time-Dependent Schoedinger Equation
• Functional integral for non-Lagrangian systems

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• Evolution and entanglement of Gaussian states in the parametric amplifier
• On the Problem of Electromagnetic-Field Quantization
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