Symplectic integrators tailored to the time-dependent Schrödinger equation
- 8 May 1996
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 104 (18) , 7099-7112
- https://doi.org/10.1063/1.471428
Abstract
We discuss and illustrate how symplectic integrators can be tailored to solve the time-dependent Schrödinger equation, yielding a large new family of wave packet propagation methods. These methods are interesting because of their algorithmic simplicity and minimal storage requirements. A variety of such methods are obtained. Calculations and comparisons with various other methods are presented for a one-dimensional Morse oscillator and a three-dimensional unimolecular dissociation problem.Keywords
This publication has 43 references indexed in Scilit:
- Numerical methods with a high order of accuracy applied in the quantum systemThe Journal of Chemical Physics, 1996
- Propagation Methods for Quantum Molecular DynamicsAnnual Review of Physical Chemistry, 1994
- Symplectic integrators for large scale molecular dynamics simulations: A comparison of several explicit methodsThe Journal of Chemical Physics, 1994
- Classical Hamiltonian structures in wave packet dynamicsThe Journal of Chemical Physics, 1994
- Hamiltonian formulation of quantum mechanics with semiclassical implications. II. Variational treatmentPhysical Review A, 1992
- The accuracy of symplectic integratorsNonlinearity, 1992
- Berry’s phase and the symplectic character of quantum time evolutionPhysical Review A, 1989
- A simplified proof of the Kosloff–Rice theorem: Intramolecular quantum dynamics cannot be chaoticThe Journal of Chemical Physics, 1989
- A b i n i t i o calculations of electronic and vibrational energies of HCO and HOCThe Journal of Chemical Physics, 1986
- The semiclassical evolution of wave packetsPhysics Reports, 1986