Global integration of the Schrödinger equation: a short iterative scheme within the wave operator formalism using discrete Fourier transforms
Abstract
A global solution of the Schrödinger equation for explicitly timedependent Hamiltonians is derived by integrating the nonlinear differential equation associated with the timedependent wave operator. A fast iterative solution method is proposed in which, however, numerous integrals over time have to be evaluated. This internal work is done using a numerical integrator based on fast Fourier transforms (FFT). The case of a transition between two potential wells of a model molecule driven by intense laser pulses is used as an illustrative example. This application reveals some interesting features of the integration technique. Each iteration provides a global approximate solution on grid points regularly distributed over the full time propagation interval. Inside the convergence radius, the complete integration is competitive with standard algorithms, especially when high accuracy is required.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 June 2015
 DOI:
 10.1088/17518113/48/22/225205
 arXiv:
 arXiv:1505.03983
 Bibcode:
 2015JPhA...48v5205L
 Keywords:

 Quantum Physics;
 Physics  Chemical Physics;
 Physics  Computational Physics
 EPrint:
 25 pages, 14 figures