Warianty tytułu
Języki publikacji
Abstrakty
A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
581-595
Opis fizyczny
Daty
wydano
2007-09-01
online
2007-05-13
Twórcy
autor
- University of Virginia, hw@virginia.edu
Bibliografia
- [1] E.J. Routh: “On some properties of certain solutions of a differential equation of second order”, Proc. London Math. Soc., Vol. 16, (1884), pp. 245–261. http://dx.doi.org/10.1112/plms/s1-16.1.245
- [2] V. Romanovski: “Sur quelques classes nouvelles de polynomes orthogonaux”, C. R. Acad. Sci. Paris, Vol. 188, (1929), pp. 1023–1025.
- [3] N. Cotfas: “Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics”, Cent. Eur. J. Phys., Vol. 2, (2004), pp. 456–466; “Shape invariant hypergeometric type operators with application to quantum mechanics”, Preprint: arXiv:math-ph/0603032. http://dx.doi.org/10.2478/BF02476425
- [4] C.B. Compean and M. Kirchbach: “The trigonometric Rosen-Morse potential in supersymmetric quantum mechanics and its exact solutions”, J. Phys. A-Math. Gen., Vol. 39, (2006), pp. 547–557. http://dx.doi.org/10.1088/0305-4470/39/3/007
- [5] A. Raposi, H.J. Weber, D. Alvarez-Castillo and M. Kirchbach: “Romanovski polynomials in selected physics problems”, Cent. Eur. J. Phys., to be published.
- [6] H.J. Weber: “Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula”, Cent. Eur. J. Math., Vol. 5, (2007), pp. 415–427. http://dx.doi.org/10.2478/s11533-007-0004-6
- [7] G.B. Arfken and H.J. Weber: Mathematical Methods for Physicists, 6th ed., Elsevier-Academic Press, Amsterdam, 2005.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-007-0014-4