Recurrence relations between transformation coefficients of hyperspherical harmonics and their application to moshinsky coefficients

Closed formulae and recurrence relations for the transformation of a two-body harmonic oscillator wave function to the hyperspherical formalism are given. With them Moshinsky or Smirnov coefficients are obtained from the transformation coefficients of hyperspherical harmonics. For these coefficients the diagonalization method of Talman and Landéreduces to simple recurrence relations which can be used directly to compute them. New closed formulae for these coefficients are also derived : they are needed to compute the two simplest coefficients which determine the sign for the recurrence relation.