The quantum quasi-invariant of the time-dependent nonlinear oscillator and application to betatron dynamics

Abstract

Both 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 figures