Renormalization-group Resummation of a Divergent Series of the Perturbative Wave Functions of Quantum Systems

Details Renormalization-group Resummation of a Divergent Series of the Perturbative Wave Functions of Quantum Systems Renormalization-group Resummation of a Divergent Series of the Perturbative Wave Functions of Quantum Systems

1998-01-29

arxiv.org/abs/hep-th/9801196v1

Prog.Theor.Phys.Suppl.131:459-470,1998

Physics

High Energy Physics

High Energy Physics - Theory

PTPTex. The needed style files are attached. 12 pages. 1 figure. Talk presented at 1997 Yukawa International Seminar (YKIS97).

Scientific paper

10.1143/PTPS.131.459

The perturbative renormalization group(RG) equation is applied to resum divergent series of perturbative wave functions of quantum anharmonic oscillator. It is found that the resummed series gives the cumulant of the naive perturbation series. It is shown that a reorganization of the resummed series reproduce the correct asymptotic form of the wave function at $x\to \infty$ when the perturbation expansion is stopped at the fourth order. A brief comment is given on the relation between the present method and the delta-expansion method, which is based on a kind of a nonperturbative RG equation.

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