Time-Dependent Approach to Reactive Scattering

Bernard Gaveau, Lawrence S. Schulman

Pascal Honvault

Jacqueline O. Berg, Charles A. Langhoff, G. Wilse Robinson

Xu‐Guang Hu, Qian-Shu Li, Au‐Chin Tang

We have formulated the quantum rearrangement scattering of atom-diatomic molecules in phase space from the viewpoint of the density operators within the framework of Torres-Vega's and Frederick's phase-space representation of quantum mechanics [J. Chem. Phys. 98, 3103 (1993); 93, 8862 (1990)]. This formalism has a remarkable feature in that it naturally includes the on-the-energy-shell coherences of the initial system that are important for depicting actual scattering experiments. We have found that the full density operator describing the rearrangement scattering is closely related not only to the usual reactive transition operator T${\mathrm{^}}_{\mathrm{\ensuremath{\beta}}\mathrm{\ensuremath{\alpha}}}$, but also to the function F defined in the paper which is nonlocal in position vector and could reflect some fine structures of the reactive scattering in strong interaction region. The time-dependent reactive scattering in the quantum phase-space representation is also discussed.

Kin’ya Takahashi, Kensuke S. Ikeda

The FFT-symplectic integrator (SI) scheme devised for solving the wave packet propagation problem is applied to stationary reactive-scattering problems. In order to relate the stationary problem to the time-dependent problem, a class of Schrödinger equation with an inhomogeneous wave source term is introduced. By using the equivalence between the stationary scattering eigenstate and the equilibrium state of the inhomogeneous Schrödinger equation, the scattering eigenstates can be computed by integrating the inhomogeneous Schrödinger equation with the FFT-SI scheme. A Gaussian wave source is proposed as an efficient wave source exhibiting rapid relaxation toward the eigenstate. Our method is tested by a one-dimensional example which has an analytical solution, and great numerical accuracy is confirmed. It is further examined by an example of time-dependent scattering and by a two-dimensional example of chaotic tunnel-scattering.

James G. Glimm, Arthur M. Jaffe