Product formula methods for time-dependent Schrodinger problems
- 21 December 1990
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 23 (24) , 5777-5793
- https://doi.org/10.1088/0305-4470/23/24/019
Abstract
The authors introduce a family of explicit and unconditionally stable algorithms for solving linear differential equations which contain a time-dependent Hermitian operator. Rigorous upper bounds are derived for two different 'time-ordered' approximation schemes and for errors resulting from approximating a time-ordered exponential by an ordinary exponential operator. The properties and the usefulness of the product formula algorithms are examined by applying them to the problem of Zener tunnelling. The most efficient algorithm is employed to solve the time-dependent Schrodinger equation for a wavepacket incident on a time-modulated rectangular barrier.Keywords
This publication has 21 references indexed in Scilit:
- Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical physicsJournal of Mathematical Physics, 1985
- Traversal Time for TunnelingPhysical Review Letters, 1982
- On the convergence of exponential operators—the Zassenhaus formula, BCH formula and systematic approximantsCommunications in Mathematical Physics, 1977
- Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problemsCommunications in Mathematical Physics, 1976
- Generalized Cumulant Expansion MethodJournal of the Physics Society Japan, 1962
- On the exponential solution of differential equations for a linear operatorCommunications on Pure and Applied Mathematics, 1954
- An Expansion Theorem of the Density MatrixThe Journal of Chemical Physics, 1952
- An Operator Calculus Having Applications in Quantum ElectrodynamicsPhysical Review B, 1951
- On Product IntegrationJournal of Mathematics and Physics, 1937
- Non-adiabatic crossing of energy levelsProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1932