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

We outline a method based on successive canonical transformations which yie lds a product expansion for the evolution operator of a general (possibly n on-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 Schroumldinger equation. We apply this method to study the dynamics of a general nondegenerate two-level quantum s ystem, a time-dependent classical harmonic oscillator, and a degenerate sys tem consisting of a spin 1 particle interacting with a time-dependent elect ric field (E) over right arrow(t) through the Stark Hamiltonian H=lambda((J ) over right arrow.(E) over right arrow)(2). (C) 1999 American Institute of Physics. [S0022-2488(99)02207-0].