  This is a challenging paper including some review and new results.
  Since the non-commutative version of the classical system based on the
compact group SU(2) has been constructed in (quant-ph/0502174) by making use of
Jaynes-Commings model and so-called Quantum Diagonalization Method in
(quant-ph/0502147), we construct a non-commutative version of the classical
system based on the non-compact group SU(1,1) by modifying the compact case.
  In this model the Hamiltonian is not hermite but pseudo hermite, which causes
a big difference between two models. For example, in the classical
representation theory of SU(1,1), unitary representations are infinite
dimensional from the starting point. Therefore, to develop a unitary theory of
non-commutative system of SU(1,1) we need an infinite number of non-commutative
systems, which means a kind of {\bf second non-commutativization}. This is a
very hard and interesting problem.
  We develop a corresponding theory though it is not always enough, and present
some challenging problems concerning how classical properties can be extended
to the non-commutative case.
  This paper is arranged for the convenience of readers as the first subsection
is based on the standard model (SU(2) system) and the next one is based on the
non-standard model (SU(1,1) system). This contrast may make the similarity and
difference between the standard and non-standard models clear.
