Local approximation to the critical parameters of quantum wells
We calculate the critical parameters for some simple quantum wells by means of the Riccati–Padé method. The original approach converges reasonably well for nonzero angular-momentum quantum number l but rather too slowly for the s states. We therefore propose a simple modification that yields remarka...
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| Autores principales: | , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2013
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/104286 http://hdl.handle.net/11336/4816 |
| Aporte de: |
| Sumario: | We calculate the critical parameters for some simple quantum wells by means of the Riccati–Padé method. The original approach converges reasonably well for nonzero angular-momentum quantum number l but rather too slowly for the s states. We therefore propose a simple modification that yields remarkably accurate results for the latter case. The rate of convergence of both methods increases with l and decreases with the radial quantum number n. We compare RPM results with WKB ones for sufficiently large values of l. As illustrative examples we choose the one-dimensional and central-field Gaussian wells as well as the Yukawa potential. The application of perturbation theory by means of the RPM to a class of rational potentials yields interesting and baffling unphysical results. |
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