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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 $ππ$, $πN$ and $NN$ elastic interactions which turns out to be competitive even for small number of grid points.