The convolution theorem and the Franck-Condon integral
Alberto José Palma, V. M. Le�n, L. Sandoval · International Journal of Quantum Chemistry · 1999
The convolution theorem is used to evaluate the Franck–Condon integral. It is shown that this integral becomes the matrix element between two “squeezed” states. This enables one to evaluate the integral by using boson operators. In addition, a general method is developed to obtain integrals involving Hermite polynomials with a displaced argument. In particular, the two-center matrix element g〈m|f(xe)|n〉e, is obtained, where f(xe)=exp(Dx+Fxe). ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 11–15, 1999