IFISUR   23398
INSTITUTO DE FISICA DEL SUR
Unidad Ejecutora - UE
artículos
Título:
Mathematical Properties of generalized Sturmians functions
Autor/es:
M. J. AMBROSIO; J.A. DEL PUNTA; K. V. RODRIGUEZ; G.GASANEO; L. U. ANCARANI
Revista:
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Editorial:
IOP PUBLISHING LTD
Referencias:
Lugar: Londres; Año: 2011 vol. 45 p. 15201 - 15222
ISSN:
1751-8113
Resumen:
We study some mathematical properties of generalized Sturmian functions which are solutions of a Schrödinger-like equation suplemented by two boundary conditions. These generalized functions, for any value of the energy,  are defined in terms of the magnitude of the potential.  One of the boundary conditions is imposed at the origin of the coordinate, where regularity is required. The second point  is at large distances. For negative energies,  bound-like conditions are imposed.  For positive or complex energies, incoming or outgoing boundary conditions are imposed to deal with scattering problems; in this case, since scattering conditions are complex, the Sturmian functions themselves are complex.  Since all of the functions solve a Sturm-Liouville problem, they allow us to construct a Sturmian basis set which must be orthogonal and complete: this is the case even when they are complex.  Here we study some properties of generalized Sturmian functions associated with the Hulthén potential,  in particular, the spatial organization of their nodes, and demonstrate explicitly their orthogonality.  We also show that the overlap matrix elements, which are generally required in scattering or bound state calculations, are well defined. Many of these mathematical  properties are expressed in terms of uncommon multivariable hypergeometric  functions. Finally,  applications to the scattering of a particle by a Yukawa and by a Hulthén potential serve as illustrations of the effieciency of the complex  Hulthén-Sturmian basis.