A differentiation formula, with application to the two-dimensional Schrödinger equation
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2014
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| _version_ | 1866911412436074496 |
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| author | Pikovski, Alexander |
| author_facet | Pikovski, Alexander |
| contents | A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent variable. This method is applied to the numerical solution of the eigenvalue problem for the two-dimensional Schrödinger equation, where standard methods converge very slowly while the approach proposed here gives accurate results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1410_5402 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | A differentiation formula, with application to the two-dimensional Schrödinger equation Pikovski, Alexander Computational Physics Numerical Analysis Quantum Physics A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent variable. This method is applied to the numerical solution of the eigenvalue problem for the two-dimensional Schrödinger equation, where standard methods converge very slowly while the approach proposed here gives accurate results. |
| title | A differentiation formula, with application to the two-dimensional Schrödinger equation |
| topic | Computational Physics Numerical Analysis Quantum Physics |
| url | https://arxiv.org/abs/1410.5402 |