GPU Implementation of the Feynman Path-Integral Method in Quantum Mechanics

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Examensarbete för kandidatexamen
Bachelor Thesis
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Publicerad
2011
Författare
Ahlén, Olof
Bohlin, Gustav
Carlsson, Kristoffer
Gren, Martin
Holmvall, Patric
Säterskog, Petter
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Sammanfattning
The Path-Integral Formulation of Quantum Mechanics is intro- duced along with a detailed mathematical description of how it is used in quantum computations. The important concept of the kernel is explained, along with the free particle and harmonic oscillator as examples. Furthermore, the method for calculating expectation values of quantum operators is explained. The expectation values are naturally calculated by importance sampled Monte Carlo integration and by use of the Metropolis al- gorithm. This is due to the discretization of the path integral results in an integral with a high number of integration variables. The math- ematical concepts of this calculation are explained. Also, a method for obtaining the probability density of the treated system is presented. The calculations are performed by a GPU, due to its high ca- pabilities for numerical operations. This requires the mathematical computations to be parallelized and is done by use of the free software PyOpenCL. A thorough introduction to these concepts are given. The resulting ground state energies and probability densities for many particle systems interacting with harmonic as well as attrac- tive and repulsive gaussian potentials are presented. The calculations worked exceedingly well for many particle systems. Source code is available at https://sourceforge.net/projects/ feynmangpu/files/
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Grundläggande vetenskaper, Fysik, Elementarpartikelfysik, Kärnfysik, Basic Sciences, Physical Sciences, Elementary particle physics, Nuclear physics
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