  We present the exact diagonalization of the Schrodinger operator
corresponding to a periodic potential with N deltas of different couplings, for
arbitrary N. This basic structure can repeat itself an infinite number of
times. Calculations of band structure can be performed with a high degree of
accuracy for an infinite chain and of the correspondent eigenlevels in the case
of a random chain. The main physical motivation is to modelate quantum wire
band structure and the calculation of the associated density of states. These
quantities show the fundamental properties we expect for periodic structures
although for low energy the band gaps follow unpredictable patterns. In the
case of random chains we find Anderson localization; we analize also the role
of the eigenstates in the localization patterns and find clear signals of
fractality in the conductance. In spite of the simplicity of the model many of
the salient features expected in a quantum wire are well reproduced.
