Is the level spacing distribution of the infinite-dimensional harmonic oscillator that of a Poisson process?

By averaging over the frequencies of the oscillations, the spacing distribution of the infinite-dimensional harmonic oscillator is shown to be e(-s), following the universal behaviour of spacing distributions of integrable systems. For oscillators of finite dimension, n, reasons for the model distribution, zeta(n)(-1)e(zeta(n)-1s), are suggested. Numerical results follow.