Typically, the interaction potential depends only on the vector r = r1 - r2 between the two particles. In that case the Schrödinger equation separates, if we change variables from r1, r2 to r and R = (m1r1 + m2r2) / (m1 + m2) (the center of mass).
(a) Show that r1 = R + (μ/m1)r, r2 = R - (μ/m2)r, and â½1=(μ/m2)â½R +â½r ,â½2 = (μ/m1) â½R â â½r, where μ = m1m2 / m1+m2 is the reduced mass of the system.