Optimized Perturbation Methods for the Free Energy of the Anharmonic Oscillator
Kostas Vlachos, Anna Okopinska
TL;DR
This paper explores optimized perturbation techniques to accurately compute the free energy of the quantum anharmonic oscillator at various temperatures, demonstrating rapid convergence and strong agreement with exact results.
Contribution
It introduces two optimized expansion methods for calculating the free energy, applicable to both quantum and classical effective potentials, with proven quick convergence and accuracy.
Findings
Methods show rapid convergence across temperature ranges.
Results agree well with exact free energy calculations.
Applicable to both quantum and classical potentials.
Abstract
Two possibile applications of the optimized expansion for the free energy of the quantum-mechanical anharmonic oscillator are discussed. The first method is for the finite temperature effective potential; the second one, for the classical effective potential. The results of both methods show a quick convergence and agree well with the exact free energy in the whole range of temperatures. Postscript figures are available under request to AO email [email protected]
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