English

Quantum Averaging I: Poincar\'e--von Zeipel is Rayleigh--Schr\"odinger

Quantum Physics 2009-10-28 v1

Abstract

An exact analogue of the method of averaging in classical mechanics is constructed for self--adjoint operators. It is shown to be completely equivalent to the usual Rayleigh--Schr\"odinger perturbation theory but gives the sums over intermediate states in closed form expressions. The anharmonic oscillator and the Henon--Heiles system are treated as examples to illustrate the quantum averaging method.

Keywords

Cite

@article{arxiv.quant-ph/9412010,
  title  = {Quantum Averaging I: Poincar\'e--von Zeipel is Rayleigh--Schr\"odinger},
  author = {Wolfgang Scherer},
  journal= {arXiv preprint arXiv:quant-ph/9412010},
  year   = {2009}
}

Comments

12 pages, LaTeX, to appear in Journ. Phys. A

R2 v1 2026-07-22T20:00:04.952Z