Extracting density information from finite Hamiltonian matrices

The approximate density-of-states information are extracted over a continuous range of energies from a finite symmetric Hamiltonian matrix. The theory of orthogonal polynomials associated with tridiagonal matrices is employed for the development of approximation schemes. Hamiltonian matrices are applied to the problems with single, double and multiple density bands. The infinite spectrum and a particle in the potential field are discussed with respect to the density information from finite Hamiltonian matrices.