AVOIDANCE OF SINGULARITIES IN MOMENTS EXPANSIONS - A NUMERICAL STUDY

The use of connected moments expansions to approximate the ground-stat e energy of many-body systems is well-known to suffer from extraneous singularities throughout parameter space, Recently Ullah has derived a n approximation based on a probability distribution function having a delta-function and a uniform distribution. The expressions obtained up to second order do not have the singularities which plague the connec ted moments expansions. In this paper, we apply the approximation of U llah to the harmonic oscillator, the anharmonic oscillator and the Kon do Hamiltonian.