Wave-number dependent current correlation for a harmonic oscillator

The wave-number k dependent current-correlation function is considered for a harmonic oscillator model. An explicit analytic expression for the Laplace transformed correlation function is derived. It is compared with numerical solutions and results obtained by the recurrence relation method. Several limiting cases such as the long-wavelength limit k→0 and the deep inelastic limit k→∞ are discussed in detail. In particular, we show that the deep inelastic limit allows for an explicit summation of the continued fraction. An approximation scheme for the recurrants at intermediate values of k is also considered.