The connected-moments polynomial approach for Hamiltonian eigenvalues calculation and its application to the one-particle systems

The new connected-moments polynomial approach (CMP) is developed for evaluation of Hamiltonian eigenvalues. It is based on properties of specially designed polynomial and does not use any basis set and variational procedure. Like all the methods based on hamiltonain moments knowledge, the CMP is conceptually simple but is less tedious and is usually convergent even for very "crude" trial functions. This method is applicable not only to the ground state energy calculation but also to the excited states. The formalism is presented in two modifications: non-local (integral) and local (integral-free) ones. An accuracy of both versions is illustrated by numerical examples of Hamiltonian eigenvalues calculations for harmonic and anharmonic oscillators. (C) 2007 Wiley Periodicals, Inc.