  Discussed is the quantized version of the classical description of collective
and internal affine modes as developed in Part I. We perform the Schr\"odinger
quantization and reduce effectively the quantized problem from $n^{2}$ to $n$
degrees of freedom. Some possible applications in nuclear physics and other
quantum many-body problems are suggested. Discussed is also the possibility of
half-integer angular momentum in composed systems of spin-less particles.
