Isospectral scattering for relativistic equivalent Hamiltonians on a coarse momentum grid

The scattering phase-shifts are invariant under unitary transformations of the Hamiltonian. However, the numerical solution of the scattering problem that requires to discretize the continuum violates this phase-shift invariance among unitarily equivalent Hamiltonians. We extend a newly found prescription for the calculation of phase shifts which relies only on the eigenvalues of a relativistic Hamiltonian and its corresponding Chebyshev angle shift. We illustrate this procedure numerically considering $\pi\pi$, $\pi N$ and $NN$ elastic interactions which turns out to be competitive even for small number of grid points.