  We study the known coherent states of a quantum harmonic oscillator from the
standpoint of the original developed noncommutative integration method for
linear partial differential equations. The application of the method is based
on the symmetry properties of the Schr\"odinger equation and on the orbit
geometry of the coadjoint representation of Lie groups. We have shown that
analogs of coherent states constructed by the noncommutative integration can be
expressed in terms of the solution of a system of differential equations on the
Lie group of the oscillatory Lie algebra. The solutions constructed are
directly related to irreducible representation of the Lie algebra on the
Hilbert space functions on the Lagrangian submanifold to the orbit of the
coadjoint representation.
