Continuum discretization using orthogonal polynomials
A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented @Phys. Rev. A 63, 052111 ~2001!#. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2003 |
| País: | España |
| Institución: | Universidad de Huelva (UHU) |
| Repositorio: | Arias Montano. Repositorio Institucional de la Universidad de Huelva |
| Idioma: | inglés |
| OAI Identifier: | oai:ariasmontano.uhu.es:10272/8133 |
| Acceso en línea: | http://hdl.handle.net/10272/8133 |
| Access Level: | acceso abierto |
| Palabra clave: | Harmonic oscillator Oscilador armónico |
| Sumario: | A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented @Phys. Rev. A 63, 052111 ~2001!#. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems. In particular, we construct wave functions that represent the continuum by making use of families of orthogonal polynomials whose weight function is the square of the ground state wave function, expressed in terms of a suitably scaled variable. As an illustration, the formalism is applied to one-dimensional Morse, Po¨schl-Teller, and square well potentials. We show how the method can deal with potentials having several bound states, and for the square well case we present a comparison of the discretized and exact continuum wave functions. |
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