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

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

1999-04-07

arxiv.org/abs/quant-ph/9904026v1

J.Math.Phys. 40 (1999) 3311-3326

Physics

Quantum Physics

19 pages, accepted for publication in J. Math. Phys

Scientific paper

10.1063/1.532889

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.

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