  In this work, we investigate the semiclassical limit of a simple bosonic
quantum many-body system exhibiting both integrable and chaotic behavior. A
classical Hamiltonian is derived using coherent states. The transition from
regularity to chaos in classical dynamics is visualized through Poincar\'e
sections. Classical trajectories in phase space closely resemble the
projections of the Husimi functions of eigenstates with similar energy, even in
chaotic cases. It is demonstrated that this correlation is more evident when
projecting the eigenstates onto the Fock states. The analysis is carried out at
a critical energy where the eigenstates are maximally delocalized in the Fock
basis. Despite the imperfect delocalization, its influence is present in the
classical and quantum properties under investigation. The study systematically
establishes quantum-classical correspondence for a bosonic many-body system
with more than two wells, even within the chaotic region.
