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Explicit integration method for the time-dependent Schrodinger equation for collision problems
Abstract
To date, only the implicit (Crank–Nicholson) integration method has ben used for numerical integration of the Schrodinger equation for collision processes. The standard explicit methods are known to be unstable and a high price is paid for the implicit method due to the inversion of the large matrices involved. Furthermore, the method is prohibitive in more than two dimensions due to restrictions on memory and large computation times. An explicit method (i.e., a method which doesn’t require the solution of simultaneous equations) is presented, and is shown to be stable in n dimensions to the same order of accuracy as the implicit method with the unitarity being secured to two orders higher accuracy than that for the wave function.
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Citations
Cited by
Manthe, U., Meyer, H.-D., & Cederbaum, L. S. (1992) · The Journal of Chemical Physics · doi:10.1063/1.463007 · Cited by 998
Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation
Choi, S., & Vaníček, J. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5092611 · Cited by 25
Metadata
- Authors
- Askar, A., & Cakmak, A. S.
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 1978-03-15
- Volume
- 68
- Issue
- 6
- Pages
- 2794-2798
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W1986219311
- Cited by
- 269
- References
- 0
- FWCI
- 1.55
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Explicit integration method for the time-dependent Schrodinger equation for collision problems. https://app.cochat.ai/papers/10.1063/1.436072
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- Askar, A., & Cakmak, A. S. (1978). Explicit integration method for the time-dependent Schrodinger equation for collision problems. The Journal of Chemical Physics. https://doi.org/10.1063/1.436072
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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