  We address the multiplicity of solutions to the time-energy canonical
commutation relation for a given Hamiltonian. Specifically, we consider a
particle spatially confined in a potential free interval, where it is known
that two distinct self-adjoint and compact time operators conjugate to the
system Hamiltonian exist. The dynamics of the eigenvectors of these operators
indicate that different time operators posses distinguishing properties that
can unambiguously associate them to specific aspects of the quantum time
problem.
