Isospectral scattering for relativistic equivalent Hamiltonians on a coarse momentum grid

Abstract

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.

18 pages, 18 figures

References in corpus (4)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Semi-spectral Chebyshev method in Quantum Mechanics
• Solving Bethe-Salpeter scattering state equation in Minkowski space
• Spectral-shift and scattering-equivalent Hamiltonians on a coarse momentum grid