dorsal/arxiv
View SchemaAn economical method to calculate eigenvalues of the Schroedinger Equation
| Authors | G. H. Rawitscher, I. Koltracht |
|---|---|
| Categories | |
| ArXiv ID | physics/0606030 |
| URL | https://arxiv.org/abs/physics/0606030 |
| DOI | 10.1088/0143-0807/27/5/017 |
Abstract
The method is an extension to negative energies of a spectral integral equation method to solve the Schroedinger equation, developed previously for scattering applications. One important innovation is a re-scaling procedure in order to compensate for the exponential behaviour of the negative energy Green's function. Another is the need to find approximate energy eigenvalues, to serve as starting values for a subsequent iteration procedure. In order to illustrate the new method, the binding energy of the He-He dimer is calculated, using the He-He TTY potential. In view of the small value of the binding energy, the wave function has to be calculated out to a distance of 3000 a.u. Two hundred mesh points were sufficient to obtain an accuracy of three significant figures for the binding energy, and with 320 mesh points the accuracy increased to six significant figures. An application to a potential with two wells separated by a barrier, is also made.
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"abstract": "The method is an extension to negative energies of a spectral integral\nequation method to solve the Schroedinger equation, developed previously for\nscattering applications. One important innovation is a re-scaling procedure in\norder to compensate for the exponential behaviour of the negative energy\nGreen\u0027s function. Another is the need to find approximate energy eigenvalues,\nto serve as starting values for a subsequent iteration procedure. In order to\nillustrate the new method, the binding energy of the He-He dimer is calculated,\nusing the He-He TTY potential. In view of the small value of the binding\nenergy, the wave function has to be calculated out to a distance of 3000 a.u.\nTwo hundred mesh points were sufficient to obtain an accuracy of three\nsignificant figures for the binding energy, and with 320 mesh points the\naccuracy increased to six significant figures. An application to a potential\nwith two wells separated by a barrier, is also made.",
"arxiv_id": "physics/0606030",
"authors": [
"G. H. Rawitscher",
"I. Koltracht"
],
"categories": [
"physics.comp-ph",
"physics.atom-ph"
],
"doi": "10.1088/0143-0807/27/5/017",
"title": "An economical method to calculate eigenvalues of the Schroedinger Equation",
"url": "https://arxiv.org/abs/physics/0606030"
},
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