Derivative expansion in the HAL QCD method for a separable potential

Abstract We investigate how the derivative expansion in HAL QCD method works to extract physical observables, using a separable potential quantum mechanics, which is solvable but highly non-local coordinate system. consider three cases for inputs determine expansion: (1) energy eigenfunctions, (2) time-dependent wave functions as solutions Schrödinger equation with some boundary conditions, and (3) function made by linear combination of finite number eigenfunctions at low mimic volume effect. have found that, all cases, potentials provide reasonable scattering phase shifts even leading order expansion, they give more accurate results increases. By comparing above those from formal potential, we conclude that not way obtain observables such binding energies, converge exact ones much faster than potential.