Testing the (t, t') method for wave packet evolution in the presence of time varying fields:

Abstract

The (t,t’) technique for quantum dynamics with general time dependent Hamiltonians is precise but time consuming to use. Using floquet basis in the (t,t’) method, the exponential of floquet matrix is to be calculated. The floquet matrix being infinitely large matrix, it is really time consuming to find the exponential of this matrix. Using Zassenhaus formula resulted as immediate consequence of Baker- Campbell- Hausdorff formula, the floquet matrix is splitted into subdiagonal and superdiagonal matrix. The analytical solution of these matrices is calculated upto third commutator. The stabilization of the Symmetric double well system is checked with the algorithm found for the exponential of hamiltonian by the split operator method.