Let L := -Δ + V be a nonnegative Schrödinger operator on L2(RN), where N ≥ 2 and V is a radially symmetric inverse square potential. In this paper we assume either L is subcritical or null-critical and we establish a method for obtaining the precise description of the large time behavior of e-tLφ, where φ ∊ L2(RN, e∣x∣2=4/dx).