  We first study a free particle on an $(n-1)$-sphere in an extended phase
space, where the originally second-class Hamiltonian and constraints are now in
strong involution. This allows for a Schr\"odinger representation and a
Hamilton-Jacobi formulation of the model. We thereby obtain the free particle
energy spectrum corresponding to that of a rigid rotator. We extend these
considerations to a modified version of the field theoretical O(3) nonlinear
sigma model, and obtain the corresponding energy spectrum as well as BRST
Lagrangian.
