An Efficient Quantum Mechanical Method for the Electronic Dynamics of the Three-Dimensional Hydrogen Atom Interacting with a Linearly Polarized Strong Laser Pulse
✍ Scribed by Hirohiko Kono; Akihisa Kita; Yukiyoshi Ohtsuki; Yuichi Fujimura
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 427 KB
- Volume
- 130
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
Various time evolution methods have been proposed such as the kinetic referenced split operator method
We present a method whereby the 3D dynamics of the electronic wave packet in a hydrogen atom can be calculated efficiently. The (KRSO) [14][15][16], the Cayley-Cranck-Nicholson method method is constructed so as to satisfy the following two require-(CCN) [17, 18], and the Peaceman-Rachford method (PR) ments: the wave function is zero at the Coulomb singular point so [19, 20] (which is a two-dimensional version of the alternatthat the numerical difficulties concerning the singularity are ing-direction implicit method [21,22]). In these methods, avoided; the coordinate system is chosen so that the differential to advance the wave function at time t to the next time operators in the Hamiltonian can be well evaluated by the 3-point finite difference formula even near the singular point. The generalstep t ϩ ⌬t (where ⌬t is the time spacing), an approximate ized cylindrical coordinate system ( , z, ) is introduced to satisfy short time propagator is operated on the wave function. the above conditions, and the value of is determined to be . The These three methods use different types of approximate Schro ¨dinger equation is discretized in time and space and solved propagators. The three approximate propagators have the by the Peaceman-Rachford method. The ϭ coodinate system helps the reduction in the number of grid points. To examine the same accuracy of order ⌬t 2 and are unitary so that the numerical stability and accuracy of our method, we first apply it to norm is strictly conserved; they are applicable to the timecases where no laser field is turned on. The errors for the ordinary dependent Hamiltonian, which suits the purpose of decylindrical coordinate system ( ϭ 1) are more than ten times as scribing the dynamical behavior of atoms and molecules large as those for ϭ . We then apply the method to the case interacting with laser pulses. These methods are, however, where the atom interacts with a linearly polarized strong laser pulse.
Our method is highly reliable and is a powerful tool for analyzing different in efficiency and accuracy (which depends on the ionization processes of the hydrogen atom. ᮊ 1997 Academic Press potential [16]).
In order to accelerate the study of the dynamics involving Rydberg-like or continuum states and to facilitate the simu-148