Group theoretical aspects of L2(R+), L2(R2) and associated Laguerre polynomials

Enrico Celeghini () and Mariano A. del Olmo ()
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Enrico Celeghini: Università di Firenze and INFN–Sezione di Firenze, Dipartimento di Fisica
Mariano A. del Olmo: Universidad de Valladolid, Dpto de Física Teórica and IMUVA

A chapter in Physical and Mathematical Aspects of Symmetries, 2017, pp 133-138 from Springer

Abstract: Abstract A ladder algebraic structure for L2(R+) which closes the Lie algebra h(1) h(1), where h(1) is the Heisenberg-Weyl algebra, is presented in terms of a basis of associated Laguerre polynomials. Using the Schwinger method, the quadratic generators that span the alternative Lie algebras so(3), so(2,1) and so(3,2) are also constructed. These families of (pseudo) orthogonal algebras also allow us to obtain unitary irreducible representations in L2(R2) similar to those in spherical harmonics.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-69164-0_19

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DOI: 10.1007/978-3-319-69164-0_19

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