DETERMINATION OF FREE-ENERGIES OF AN OSCILLATOR WITH MIXED QUARTIC AND SEXTIC ANHARMONICITIES

The free energies for the oscillators with quartic, sextic, and mixed quartic-sextic anharmonicities have been calculated over a wide range of anharmocity parameter and of temperature employing the approximation methods put forward by Buttner and Flytzanis [Phys. Rev. A 36, 3443 (1987)] and by Feynman and Kleinert [Phys. Rev. A 34, 5080 (1986)]. A comparison of these values with the exact ones shows that the prescription given by Feynman and Kleinert is far superior, and that it produces quite accurate results for the potentials and temperatures considered here. The success of the Buttner-Flytzanis technique at 0 K and its failure at the intermediate as well as the high temperatures have also been analyzed.