Generalized adiabatic product expansion: a nonperturbative method of solving the time-dependent Schrodinger equation

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 Schrödinger 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 = λ(J→ · ℰ→)2.