  . The choice of a suitable random matrix model of a complex system is very
sensitive to the nature of its complexity. The statistical spectral analysis of
various complex systems requires, therefore, a thorough probing of a wide range
of random matrix ensembles which is not an easy task. It is highly desirable,
if possible, to identify a common mathematcal structure among all the ensembles
and analyze it to gain information about the ensemble- properties. Our
successful search in this direction leads to Calogero Hamiltonian, a
one-dimensional quantum hamiltonian with inverse-square interaction, as the
common base. This is because both, the eigenvalues of the ensembles, and, a
general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary
initial conditions. The varying nature of the complexity is reflected in the
different form of the evolution parameter in each case. A complete
investigation of Calogero Hamiltonian can then help us in the spectral analysis
of complex systems.
