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Variational method for the free-energy approximation of generalized anharmonic oscillators.

A variational method that uses the frequency and the energy shift as variational parameters is presented. The quantum-mechanical partition function is approximated by a formally simple expression, for a generalized anharmonic oscillator in one and many dimensions. The numerical calculations for a single quartic and two coupled quartic oscillators lead to nearly exact values for the free energy, the ground state, and the difference between the ground state and the first excited state.