Quantum spectrum of a chain of oscillators

We analyze some statistical properties in the quantum spectrum of a chain of linear oscillators. Although completely integrable, the classical version of this system exhibits very complicated motion. Studying the energy‐spacing distribution of the quantum problem we find that, for a large number of oscillators, the spectrum shows the typical characteristics of an integrable system, and conclude that no signs of the classical complicated behavior appear at quantum level. We also point out that the energy‐spacing distribution is not stationary as the energy grows. This analysis—complete with a comparison of our results with those for a particle in an N‐dimensional box—contains several points of pedagogical interest.