The rotational-dependent potential for a dissociative state is represented by U(r)=U0+B1/r +B2/r2+[N(N+1)−Λ2]/2Mr2. An analytical solution ψE(r) of the Schrödinger radial equation, valid for all regions of internuclear distance r and energy E, is obtained in terms of confluent hypergeometric function of the complex arguments. The solution is evaluated by expanding the confluent hypergeometric function onto a basis set of shifted Chebyshev polynomials. The expansion coefficients are recovered by a backward recursion technique. The summation process of Chebyshev polynomials converts a slowly convergent series or a divergent asymptotic series into a rapidly convergent one. The solution thus obtained is applied to calculate the vibrational wave function of the dissociative b 3Σ+u state of H2 to compare with the previous semiclassical WKB wave function. The solution of the rotational-corrected Morse potential is used for the upper bound c 3Πu state. The bound-continuum Frank–Condon overlap amplitude is computed as a function of energy E for different rotational quantum numbers N. Its dependence on N is found to be significant for large N. The decay rate of the metastable c 3Π+u (v=0), via perturbative mixing with b 3Σ+u, computed here with exact wave functions, is an order of magnitude smaller than the previous semiclassical value. However, the decay rate via forbidden radiative transitions to b 3Σ+u is close to the previous value. Radiative transition to b 3Σ+u is now believed to be the predominant decay mode of the metastable c 3Π+u state (at v=0). Lifetimes of the fine structure levels of N=1 and N=2 obtained are 1.00 ms for J=N and 1.31–1.32 ms for J=N±1. The lifetimes of the predissociative c 3Π−u (v=0) state are 2.33×10−8 s for N=1 and 7.65×10−9 s for N=2.