A simplified method for calculations of collective excitation energies in realistic many-fermion systems is developed. As a preliminary test of the method calculations were performed on the electron gas with encouraging results.
The basic idea of the Lanczos method is to construct a special basis where the Hamiltonian has a tridiagonal representation. Once in this form, the matrix can be diagonalized easily using standard library subroutines. This approach is known as the standard Lanczos technique (SLT) which still has the problem of diagonalizing large matrix sizes emanating from increase of the size of the Hilbert space with the size of the system. In this current presentation, we develop a simplified formulation of the SLT and then use it to study the rapid convergence to the ground state energy and wavefunction of some finite systems.