An analytical expression for the phase shift contribution to the internal partition function for the Morse potential is derived by using an approximate Jost function. This function is shown to be a convergent sum. The numerical results obtained for H₂ and HCl show the partition function to be a monotonically increasing function of temperature. This observation agrees with the results of Rogers and co-workers.

We derive an off-energy-shell generalization of the two-potential formula by using a coordinate-space approach and apply the formalism to construct algorithms for studying spatial behaviour of the fully off-shellT matrix. We also suggest some future applications of the proposed theory.