  Motivated by a canonical, QCD Hamiltonian we propose an effective Hamiltonian
to represent an arbitrary number of quarks in hadronic bags. The structure of
the effective Hamiltonian is discussed and the BCS-type solutions that may
represent constituent quarks are presented. The single particle orbitals are
chosen as 3-dimensional harmonic oscillators and we discuss a class of exact
solutions that can be obtained when a subset of single-particle basis states is
restricted to include a certain number of orbital excitations. The general
problem, which includes all possible orbital states, can also be solved by
combining analytical and numerical methods.
