  In this paper we follow the Schwinger approach for angular momentum but with
the polar basis of harmonic oscillator as a starting point. We derive by a new
method two analytic expressions of the elements of passage matrix from the
double polar basis to 4- dimensions polar basis of the harmonic oscillator.
These expressions are functions of the modules of magnetic moments. The
connection between our results and the results derived by the group theory of
Laguerre polynomials is found. We determine a new expression for these elements
in terms of magnetic moments in the general case. We deduce from these
expressions the symmetries of 3j symbols. A new generating function of the
Clebsh-Gordan coefficients, functions of the modules of magnetic moments are
found. We prove that the generating function of recoupling coefficients 3nj for
the polar basis are the same in the Schwinger's approach therefore the polar
basis of harmonic oscillator may be a starting point to study the angular
momentum.
