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Numerical Quantum Dynamics
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

We consider computational methods for simulating the dynamics of molecular systems governed by the time-dependent Schrödinger equation. Solving the Schrödinger equation numerically poses a challenge due to its often highly oscillatory solutions, and to the exponential growth of work and memory with the number of particles in the system.

Two different classes of problems are studied: the dynamics of the nuclei in a molecule and the dynamics of an electron in orbit around a nucleus. For the first class of problems we present new computational methods which exploit the relation between quantum and classical dynamics in order to make the computations more efficient. For the second class of problems, the lack of regularity in the solution poses a computational challenge. Using knowledge of the non-smooth features of the solution we construct a new method with two orders higher accuracy than what is achieved by direct application of a difference stencil.

Place, publisher, year, edition, pages
Uppsala University, 2013.
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2013-005
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
URN: urn:nbn:se:uu:diva-208837OAI: oai:DiVA.org:uu-208837DiVA: diva2:654844
Supervisors
Projects
eSSENCE
Available from: 2013-10-15 Created: 2013-10-08 Last updated: 2017-08-31Bibliographically approved
List of papers
1. An adaptive pseudospectral method for wave packet dynamics
Open this publication in new window or tab >>An adaptive pseudospectral method for wave packet dynamics
2012 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 137, 044111:1-12 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-179058 (URN)10.1063/1.4737893 (DOI)000307611500012 ()
Projects
eSSENCE
Available from: 2012-07-26 Created: 2012-08-06 Last updated: 2017-12-07Bibliographically approved
2. Coupling of Gaussian beam and finite difference solvers for semiclassical Schrödinger equations
Open this publication in new window or tab >>Coupling of Gaussian beam and finite difference solvers for semiclassical Schrödinger equations
2013 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2013-019
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-208501 (URN)
Projects
eSSENCE
Available from: 2013-09-29 Created: 2013-10-01 Last updated: 2013-10-08Bibliographically approved
3. Accelerated convergence for Schrödinger equations with non-smooth potentials
Open this publication in new window or tab >>Accelerated convergence for Schrödinger equations with non-smooth potentials
2013 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2013-007
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-198253 (URN)
Projects
eSSENCE
Available from: 2013-04-10 Created: 2013-04-10 Last updated: 2013-10-08Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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Output format
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