  In this work, using the noncommutative integration method of linear
differential equations, we obtain a complete set of solutions to the
Schrodinger equation for a quantum asymmetric top in Euler angles. It is shown
that the noncommutative reduction of the Schrodinger equation leads to the Lame
equation. The resulting set of solutions is determined by the Lame polynomials
in a complex parameter, which is related to the geometry of the orbits of the
coadjoint representation of the rotation group. The spectrum of an asymmetric
top is obtained from the condition that the solutions are invariant with
respect to a special irreducible $\lambda$-representation of the rotation
group.
