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Generalized Adiabatic Product Expansion: A nonperturbative method of solving time-dependent Schroedinger equation

By Ali Mostafazadeh

Abstract

We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion involves a finite number of terms, and our method gives the exact solution of the corresponding time-dependent Schroedinger equation. We apply this method to study the dynamics of a general nondegenerate two-level quantum system, a time-dependent classical harmonic oscillator, and a degenerate system consisting of a spin 1 particle interacting with a time-dependent electric field E(t) through the Stark Hamiltonian H=\lambda [J.E(t)]^2.Comment: 19 pages, accepted for publication in J. Math. Phy

Topics: Quantum Physics, General Relativity and Quantum Cosmology, High Energy Physics - Theory
Publisher: 'AIP Publishing'
Year: 1999
DOI identifier: 10.1063/1.532889
OAI identifier: oai:arXiv.org:quant-ph/9904026

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