2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/87899Both the classical and quantum approximate invariants are found for the nonlinar r time-dependent oscillator of sextupole transverse betatron dynamics. They are represented in terms of the elements of a Lie algebra associated with powers of phase space coordinates. The first order quantum correction to the classical quasi-invariant is found.22 pages, Two postscript figuresAccelerator PhysicsQuantum Physicstext