  In this work we derive the Hamiltonian formalism of the O(N) non-linear sigma
model in its original version as a second-class constrained field theory and
then as a first-class constrained field theory. We treat the model as a
second-class constrained field theory by two different methods: the
unconstrained and the Dirac second-class formalisms. We show that the
Hamiltonians for all these versions of the model are equivalent. Then, for a
particular factor-ordering choice, we write the functional Schrodinger equation
for each derived Hamiltonian. We show that they are all identical which
justifies our factor-ordering choice and opens the way for a future
quantization of the model via the functional Schrodinger representation.
