We examine the properties of the wave-function-equivalent potentials
which HAL QCD collaboration has introduced.
We generalize the derivative expansion, and then apply it to
energy-independent and non-local potentials in a coupled-channel
We observe that the expansion converges by comparing the scattering
phase shifts computed from these potentials with the exact one.
We have also found that the convergence can be improved by either
varying the choice of interpolating fields or tuning the expansion
scale in the generalized derivative expansion.
The results will be utilized in future lattice QCD calculations,
allowing for further application of the HAL QCD method.