Canonical perturbation expansions to large order from classical hypervirial and Hellmann-Feynman theorems.

Details Canonical perturbation expansions to large order from classical hypervirial and Hellmann-Feynman theorems. Canonical perturbation expansions to large order from classical hypervirial and Hellmann-Feynman theorems.

Sep 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992jmp....33.3004m&link_type=abstract

Journal of Mathematical Physics, Vol. 33, No. 9, p. 3004 - 3024

Mathematics

Mathematical Physics

16

Scientific paper

The classical hypervirial and Hellmann-Feynman theorems are used to formulate a "perturbation theory without Fourier series" that can be used to generate canonical series expansions for the energies of perturbed periodic orbits for separable classical Hamiltonians. Here, the method is applied to one-dimensional anharmonic oscillators and radial Kepler problems. In all cases, the classical series for energies and expectation values are seen to correspond to the expansions associated with their quantum mechanical counterparts through an appropriate action preserving classical limit. This "action fixing" is inherent in the classical Hellmann-Feynman theorem applied to periodic orbits.

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