In English

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

Olof Ahlén ; Gustav Bohlin ; Kristoffer Carlsson ; Martin Gren ; Patric Holmvall ; Petter Säterskog
Göteborg : Chalmers tekniska högskola, 2011.
[Examensarbete för kandidatexamen]

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 feynmangpu/files/

Publikationen registrerades 2011-08-11. Den ändrades senast 2013-01-08

CPL ID: 144105

Detta är en tjänst från Chalmers bibliotek