  A novel integral representation for scattering phase shifts is obtained based
on a modified version of Milne's phase-amplitude approach [W.E. Milne, Phys.
Rev. $\mathbf{35}$, 863 (1930)]. We replace Milne's nonlinear differential
equation for the amplitude function $y$ with an equivalent linear equation for
the envelope $\rho=y^2$, which renders the integral representations highly
amenable to numerical implementations. The phase shift is obtained directly
from Milne's phase function, which in turn is expressed in terms of the
envelope function. The integral representation presented in this work is fully
general and it can be used for any type of scattering potential, including the
Coulomb potential.
