Computing singularities of perturbation series

Details Computing singularities of perturbation series Computing singularities of perturbation series

2010-09-15

arxiv.org/abs/1009.2901v1

Physics

Quantum Physics

11 figures, submitted

Scientific paper

Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the perturbed Hamiltonian on a vector, and does not rely on the terms in the perturbation series. Some illustrative model problems are studied, including a Helium-like model with $\delta$-function interactions for which M{\o}ller--Plesset perturbation theory is considered and the radius of convergence found.

Affiliated with

Also associated with

No associations

Rating

Computing singularities of perturbation series does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Computing singularities of perturbation series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computing singularities of perturbation series will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-77268