dorsal/arxiv
View SchemaComments on the Discrete Variable Representation
| Authors | Barry I. Schneider, Nicolai Nygaard |
|---|---|
| Categories | |
| ArXiv ID | physics/0407076 |
| URL | https://arxiv.org/abs/physics/0407076 |
| DOI | 10.1103/PhysRevE.70.056706 |
| Journal | Phys. Rev. E 70, 056706 (2004) |
Abstract
We discuss the application of the Discrete Variable Representation to Schr\"odinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well-behaved, the boundary conditions are satisfied and the calculation is rapidly convergent. The accuracy of the method is demonstrated by applying it to the hydrogen atom. We emphasize that the method is equally capable of describing bound states and continuum solutions.
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"abstract": "We discuss the application of the Discrete Variable Representation to\nSchr\\\"odinger problems which involve singular Hamiltonians. Unlike recent\nauthors who invoke transformations to rid the eigenvalue equation of\nsingularities at the cost of added complexity, we show that an approach based\nsolely on an orthogonal polynomial basis is adequate, provided the\nGauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the\nmesh contains the singular points and by simply discarding the DVR functions\ncorresponding to those points, all matrix elements become well-behaved, the\nboundary conditions are satisfied and the calculation is rapidly convergent.\nThe accuracy of the method is demonstrated by applying it to the hydrogen atom.\nWe emphasize that the method is equally capable of describing bound states and\ncontinuum solutions.",
"arxiv_id": "physics/0407076",
"authors": [
"Barry I. Schneider",
"Nicolai Nygaard"
],
"categories": [
"physics.chem-ph",
"physics.comp-ph"
],
"doi": "10.1103/PhysRevE.70.056706",
"journal_ref": "Phys. Rev. E 70, 056706 (2004)",
"title": "Comments on the Discrete Variable Representation",
"url": "https://arxiv.org/abs/physics/0407076"
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