  An exact quantization of the spherical membrane moving in flat target
spacetime backgrounds is performed. Crucial ingredients are the exact
integrabilty of the $3D~SU(\infty)$ continuous Toda equation and the
quasi-finite highest weight irreducible representations of $W_{\infty}$
algebras. Both continuous and discrete energy levels are found. The latter are
found for periodic-like solutions. Membrane wavefunctionals solutions are found
in terms of Bessel's functions and plausible relations to singleton field
theory are outlined.
