On the hydrogen wave function in Momentum-space, Clifford algebra and the Generating function of Gegenbauer polynomial

Mehdi Hage-Hassan (1)

1 UL - Faculté des Sciences Section (1)

Using the quadratic transformation and the generating function method we Perform the Fourier transformation of the wave function of coordinates of hydrogen atom and we find the analytic expression of the wave function in momentum space. We derive the matrix elements between the basis to 4-dimensions and integral representation of the generating functions of Gegenbauer polynomials. We find a relationship between a class of Clifford algebra and the generating functions of these polynomials.

Mots clés: hydrogen atom; Momentum-space; Clifford algebra; Kustaanheimo-Steifel transformation

Domaines: Physique Quantique [quant-ph]; Physique mathématique [math-ph]

Mehdi Hage-Hassan. On the hydrogen wave function in Momentum-space, Clifford algebra and the Generating function of Gegenbauer polynomial. 2008. ⟨hal-00305330⟩