Observables of the three body Coulomb Problem
The Coulomb three body problem is solved using a variational approach. We consider only S-wave solutions in this work. The wave function is expanded in products of Laguerre polynomials which are coordinate functions of perimetric coordinates. These choices follow from the work of Liverts and Barnea...
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Florida State Open Publishing
2020-11-01
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| Series: | The Owl |
| Online Access: | https://journals.flvc.org/owl/article/view/119025 |
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doaj-2f1ef00331a34decada9e8666ffbf3132021-04-01T18:38:01ZengFlorida State Open PublishingThe Owl2693-57592693-57832020-11-01101Observables of the three body Coulomb ProblemShae Machlus0Department of Physics The Coulomb three body problem is solved using a variational approach. We consider only S-wave solutions in this work. The wave function is expanded in products of Laguerre polynomials which are coordinate functions of perimetric coordinates. These choices follow from the work of Liverts and Barnea, whose Mathematica code was used for the calculation of energy and wave function coefficients. Observables of Helium are calculated for a single and seven state wave function expansion. Additionally, for the single state problem, the energy correction due to the finite size of alpha particle is calculated and determined to be negligible. There is agreement between the results of this work and that of similar literature. Future work includes a resolution study of the expectation values as a function of the wave function expansion size. https://journals.flvc.org/owl/article/view/119025 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Shae Machlus |
| spellingShingle |
Shae Machlus Observables of the three body Coulomb Problem The Owl |
| author_facet |
Shae Machlus |
| author_sort |
Shae Machlus |
| title |
Observables of the three body Coulomb Problem |
| title_short |
Observables of the three body Coulomb Problem |
| title_full |
Observables of the three body Coulomb Problem |
| title_fullStr |
Observables of the three body Coulomb Problem |
| title_full_unstemmed |
Observables of the three body Coulomb Problem |
| title_sort |
observables of the three body coulomb problem |
| publisher |
Florida State Open Publishing |
| series |
The Owl |
| issn |
2693-5759 2693-5783 |
| publishDate |
2020-11-01 |
| description |
The Coulomb three body problem is solved using a variational approach. We consider only S-wave solutions in this work. The wave function is expanded in products of Laguerre polynomials which are coordinate functions of perimetric coordinates. These choices follow from the work of Liverts and Barnea, whose Mathematica code was used for the calculation of energy and wave function coefficients. Observables of Helium are calculated for a single and seven state wave function expansion. Additionally, for the single state problem, the energy correction due to the finite size of alpha particle is calculated and determined to be negligible. There is agreement between the results of this work and that of similar literature. Future work includes a resolution study of the expectation values as a function of the wave function expansion size.
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| url |
https://journals.flvc.org/owl/article/view/119025 |
| work_keys_str_mv |
AT shaemachlus observablesofthethreebodycoulombproblem |
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