Dynamical invariants for variable quadratic Hamiltonians

2010/02/28 by Sergei K. Suslov, Sergei K Suslov
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Eigenfunction #Eigenvalues and eigenvectors #Invariant (physics) #Mathematical and Computational Methods #Nonlinear Waves and Solitons #Nonlinear system #Quadratic equation #Schrödinger equation #Superposition principle #Variable (mathematics) #math-ph #math.MP

paper · pdf · doi:10.1088/0031-8949/81/05/055006

21 pages, no figures; to appear in Physica Scripta

arxiv created 2010/03/11 · openalex publication_date 2010/05/01 · arxiv updated 2015/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

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.

Citations

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