Spectral autocorrelation function in the statistical theory of energy levels

The spectral autocorrelation function is evaluated analytically for the Gaussian ensembles of Hamiltonian matrices. A direct comparison of the prediction of these ensembles with experimentally measured spectra is thereby possible. Also computed is the time autocorrelation function of an initially prepared nonstationary state. The repulsion of eigenstates in the time domain is clearly manifested in the analytic result.