# Chapter 6: Correlation Functions and Spectra

Autocorrelation function and spectrum of a displaced Gaussian in a harmonic potential (analytic).

This program calculates the autocorrelation function of a displaced Gaussian in a harmonic potential, using the analytic formula:

where is the so-called dimensionless displacement of the center of the coherent state from the minimum of the harmonic potential A window function is used to smoothly cut off C(t). The Fourier transform of the correlation function is used to calculate the electronic absorption spectrum. The idealized line spectrum is given by a Poisson distribution:

This program calculates the autocorrelation function of a displaced Gaussian in a harmonic potential, using the analytic formula:

where is the so-called dimensionless displacement of the center of the coherent state from the minimum of the harmonic potential A window function is used to smoothly cut off C(t). The Fourier transform of the correlation function is used to calculate the electronic absorption spectrum. The idealized line spectrum is given by a Poisson distribution: