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We use—after a shift transformation of the variable—the Burrows, Cohen and Feldmann approximation procedure to solve the problem of finding the energy eigenvalues for an anharmonic oscillator with cubic and quartic terms subjected to a linear external potential. Both low- and high-frequency limits are considered. A first application is given by deriving (in the high-frequency case) the partition function of a gas composed of such anharmonic oscillators. We also exploit the recently proved formal equivalence between a high-frequency anharmonic oscillator (in the approximation considered) and an infinitesimally deformed harmonic oscillator to introduce SU(2) and SU(1,1) algebras for the anharmonic oscillator with cubic and quartic terms.

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