VARIATIONAL EFFECTIVE-HAMILTONIANS AS A GENERALIZATION OF THE RAYLEIGH QUOTIENT

Taking advantage of the generalized variational principle, previously introduced alternative effective Hamiltonians are shown to satisfy variational properties for the lowest energies. Geometrical and arithmetical properties establishing connections with the Rayleigh quotient are emphasized. An illustration of the considerable improvement in convergence properties, obtained by their use in perturbative and iterative expansions, is given by an application to the Mathieu equation.