We present the full set of equations for the solution of the trinucleon problem by the hyperspherical harmonics expansion (HHE) method where nucleons interact via the Reid soft core (RSC) potential. The coupling potential matrix elements are expressed in terms of geometrical structure coefficients (GSC) and potential multipoles (PM). Introduction of GSC greatly simplifies the calculation of the potential matrix and makes the numerical algorithm efficient. A method for calculating all the twelve independent sets of GSC needed, by using the completeness property of the Jacobi polynomials has been presented. A convenient sum rule for each set of GSC has also been derived and precision of the calculated GSC has been checked by the sum rule. Such calculations of GSC are efficient and fast, in view of the complexity of the HHE equations.

The hyperspherical harmonics expansion method has been used to solve the trinucleon system where the nucleons interact through Reid soft core potential. The binding energy of triton, both for extreme adiabatic approximation and uncoupled adiabatic approximation, and theS-state,S′-state andD-state probabilities are calculated and compared with the results by the Faddeev method.