Group theoretical aspects of $L^2({\mathbb{R}}^{+})$, $L^2({\mathbb{R}}^2)$ and associated Laguerre polynomials

E. Celeghini, M. A. del Olmo

A ladder algebraic structure for $L^2({\mathbb{R}}^{+})$ which closes the Lie algebra $h(1)\oplus h(1)$, where $h(1)$ is the Heisenberg-Weyl algebra, is presented in terms of a basis o…