The SL(2,R) WZNW → Liouville reduction leads to a nontrivial
phase space on the classical level both in 0+1 and 1+1 dimensions. To study
the consequences in the quantum theory, the quantum mechanics of the 0+1
dimensional, point particle version of the constrained WZNW model is
investigated. The spectrum and the eigenfunctions of the obtained---rather
nontrivial---theory are given, and the physical connection between the pieces
of the reduced configuration space is discussed in all the possible cases of
the constraint parameters.Comment: LaTeX file, 33 pages. Results extended, contains all technical
information not detailed in version to appear in J. Math. Phy