  As examples of models having interesting constraint structures, we derive a
quantum mechanical model from the spatial freezing of a well known relativistic
field theory - the chiral Schwinger model. We apply the Hamiltonian constraint
analysis of Dirac [1] and find that the nature of constraints depends
critically on a $c$-number parameter present in the model. Thus a change in the
parameter alters the number of dynamical modes in an abrupt and
non-perturbative way.
  We have obtained new {\it{real}} energy levels for the quantum mechanical
model as we explore {\it{complex}} domains in the parameter space. These were
forbidden in the parent chiral Schwinger field theory where the analogue
Jackiw-Rajaraman parameter is restricted to be real. We explicitly show
existence of modes that satisfy higher derivative Pais-Uhlenbeck form of
dynamics [3].
  We also show that the Cranking Model [7], well known in Nuclear Physics, can
be interpreted as a spatially frozen version of another well studied
relativistic field theory in 2+1-dimension- the Maxwell-Chern-Simons-Proca
Model [8].
