Wave-operator equations associated with the determination of effective Hamiltonians are generally solved by perturbation methods. However, it is well known that for most actual systems the standard Rayleigh-Schrodinger and Brillouin-Wigner series either converge slowly or diverge. One way how to deal with this problem is to modify or to renormalize the standard wave equations. For that purpose, we derive new derivative and convergence superoperators within the two basic Rayleigh-Schrodinger and Brillouin-Wiper formalisms. Since the direct use of these superoperators would imply difficult operator inversions, we investigate the efficiency of various approximations of these superoperators. It is shown that these approximations can overcome convergence difficulties and also open the way to systematic infinite partial summation schemes. A numerical illustration is presented for a model system of N non-interacting hydrogen molecules. Finally, it is shown that the determination of regular two-component relativistic Hamiltonians is also relevant to this approach. 0 1996 John Wiley & Sons, Inc.
nians. This will be done by introducing new derivative and convergence superoperators which are able to predict and extend the convergence properties of the standard Rayleigh-Schrodinger and Brillouin-Wigner schemes.
The article is organized as follows: The notations and the basic wave operator equations are recalled in the following section. Modified waveoperator equations will be given in the third seetion. Finally, a numerical illustration will be pre-T