Exact results for the statistical thermodynamics of the asymmetric single- and double-well anharmonic oscillator

Abstract

Exact analytical results are presented for the high-temperature behaviour of the anharmonic oscillator with Ĥ = p̂ 2/2m + k 2x̂ 2 + k 3^x 3 + k 4x̂ 4, k 4 > 0. The classical partition function and the exact Golden-Thompson upper bound with and without variation of the harmonic frequency are calculated for both single- and double-well oscillators.