Bound and resonance states by a time-independent filter diagonalization method for large Hamiltonian systems

A new algorithm on the basis of Neuhauser–Mandelshtam–Taylor developments of the filter diagonalization method is proposed for calculating highly excited bound states and resonances for large Hamiltonian systems, even in the high-density-state part of the spectrum. This is a complementary method to the Lanczos procedure with no reorthogonalization which is widely used for calculating the low lying energy levels, i.e. the low-density part of the spectrum. An illustrative numerical example is given.