Romanovski polynomials in selected physics problems

• Autorzy: Alvaro Raposo , Hans Weber , David Alvarez-Castillo , Mariana Kirchbach
• Języki publikacji: EN

Abstrakty

EN

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.

Słowa kluczowe

EN

Romanovski polynomials; Scarf potential; Rosen-Morse potential and random matrices; orthogonality; 02.30.Gp; 02.30.Hq; 02.30.Jr; 03.65.Ge

• Czasopismo: Open Physics
• Rocznik: 2007
• Tom: 5
• Numer: 3
• Strony: 253-284

Daty

wydano

2007-09-01

online

2007-09-01

Twórcy

autor

Alvaro Raposo

• Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, México

autor

Hans Weber

• Department of Physics, University of Virginia, Charlottesville, VA, 22904, USA,

autor

David Alvarez-Castillo

• Instituto de Física, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, México

autor

Mariana Kirchbach

• Instituto de Física, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, México

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Identyfikatory

DOI

10.2478/s11534-007-0018-5