Continuum discretization using orthogonal polynomials

Journal Article · Thu May 01 04:00:00 EDT 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.67.052108· OSTI ID:20636347

Perez-Bernal, F; Martel, I ^[1]; Arias, J M; Gomez-Camacho, J ^[2]

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1. Departamento de Fisica Aplicada, Universidad de Huelva, 21071 Huelva (Spain)
2. Departamento de Fisica Atomica, Molecular y Nuclear, Facultad de Fisica, Universidad de Sevilla, Apartado 1065, 41080 Sevilla (Spain)

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, Poeschl-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.

• OSTI ID: 20636347
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 67; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
BOUND STATE
COMPARATIVE EVALUATIONS
GROUND STATES
HARMONIC OSCILLATORS
MORSE POTENTIAL
ONE-DIMENSIONAL CALCULATIONS
POLYNOMIALS
QUANTUM MECHANICS
SQUARE-WELL POTENTIAL
WAVE FUNCTIONS
WEIGHTING FUNCTIONS