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Numerical approaches to solving the time-dependent Schrödinger equation with different potentials
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, Division of Scientific Computing.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
2016 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This project is an immersive study in numerical methods, focusing on quantum molecular dynamics and methods for solving the time-dependent Schrödinger equation. First the Schrödinger equation was solved with finite differences and a basic propagator in time, and it was then concluded that this method is far too slow and compuationally heavy for its use to be justified for this type of problem. Instead pseudo-spectral methods with split-operators were implemented, and this proved to be a far more favourable method for solving, both in regards to time and memory requirements. Further, the pseudo-spectral methods with splitoperators were used to solve the dynamics resulting from the excitation of sodium iodide by an ultra-fast laser pulse. This was modeled as two Schrödinger equations coupled with a potential modeling the laser pulse. The resulting solution made the quantum nature of the system clear, but also the limitations and advantages of different numerical methods.

Place, publisher, year, edition, pages
2016. , 22 p.
Series
TVE, 16 040 juni
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:uu:diva-295932OAI: oai:DiVA.org:uu-295932DiVA: diva2:935561
Educational program
Master Programme in Engineering Physics
Supervisors
Examiners
Available from: 2016-06-15 Created: 2016-06-10 Last updated: 2016-06-15Bibliographically approved

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