Low-order polynomial approximation of propagators for the time-dependent Schroedinger equation

Journal Article · Sun Mar 01 04:00:00 EST 1992 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1016/0021-9991(92)90318-S· OSTI ID:7307454

Tal-Ezer, H ^[1]; Kosloff, R ^[2]; Cerjan, C ^[3]

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1. Tel Aviv Univ. (Israel)
2. Fritz Haber Institute, Jerusalem (Israel)
3. Lawrence Livermore National Lab., Livermore, CA (United States)

Polynomial approximations for propagating the time-dependent Schroedinger equation are studied. These methods are motivated by the numerical demands of systems with time-dependent Hamiltonian operators. First-order and second-order Magnus expansions are tested for approximating the time ordering operator. The polynomials considered are based on a reduced basis space which is obtained by iterating the Hamiltonian operator on a initial wavefunction. The approximate polynomials are obtained by minimizing the error in the propagation. One such approach which minimizes the residuum outside the reduced space is proved to be equivalent to the short time iterative Lanczos procedure. A second approach which uses a different optimization scheme (the residuum method) is found to be somewhat superior to the Lanczos procedure. Numerical examples are used to illustrate the convergence of these methods. The second-order Magnus approximation is found to be a significant improvement over the first-order approximation regardless of method. 16 refs., 44 figs.

• OSTI ID: 7307454
• Journal Information: Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 100:1; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

664300* -- Atomic & Molecular Physics-- Collision Phenomena-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
COMPUTERIZED SIMULATION
DATA COVARIANCES
DIFFERENTIAL EQUATIONS
EQUATIONS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
SIMULATION
WAVE EQUATIONS