Using the best approximation of the time evolution operator of a quartic oscillator in the high-frequency limit, we derive its equation of the motion in the Heisenberg picture and show that such an anharmonic oscillator admits a wider class of constants of the motion than the standard harmonic oscillator.
Defalco, L., Mignani, R., Scipioni, R. (1997). Heisenberg equation and constants of the motion for an anharmonic oscillator in the high-frequency limit. IL NUOVO CIMENTO DELLA SOCIETÀ ITALIANA DI FISICA. B, GENERAL PHYSICS, RELATIVITY, ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS, 112(6), 929-931.