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| author | Ian M. Lowry |
| title | Computational Efficacy of Hamiltonian Moments-based Methods for the Calculation of Non-Tractable Potentials |
| abstract | Two versions of the connected moments expansion, those commonly known as the CMX-HW and the CMX-LT, as well as Lanczos
tri-diagonalization were computed up to 7th order for the ground state and first excited state of the anharmonic oscillator with V = x2 + Λx4.
There is no exact solution for this potential, and so it can only be approximated numerically. Trial wave functions for each method were pre-conditioned by using
variational analysis. The results were compared to previously published figures, and the computation times to each other. Lanczos tri-diagonalization was found to
be the most accurate and quickest method, with CMX-LT matching its accuracy but being far slower, and CMX-HW being slightly less accurate and taking similar time
to CMX-LT. The first excited state for both connected moments expansions was more accurate and quicker than the ground state, however the first excited state in
Lanczos tri-diagonalization had extremely poor accuracy. The preconditioning was found to improve the accuracy of the calculation by more than two orders of
magnitude. Additionally, a brief study of trial wave function kurtoses was conducted, which found no systematic effect of kurtosis on the accuracy of the
approximation. All calculations were carried out in Mathematica 9.0 run on a laptop computer.
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| school | The College of Liberal Arts, Drew University |
| degree | B.A. (2015) |
| advisor | Dr. Robert Murawski |
| committee | Professor Scott Bonn
Dr. Minjoon Kouh
Professor Steve Surace |
| full text | IMLowry.pdf |
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