An operator approach to the construction of generating functions for the product of Laguerre polynomials: the thermal average bandshape function of a molecule

We introduce two different forms of mathematical identities, involving the product of Laguerre polynomials. These identities are a direct reflection of an operator identity. It is shown that these relations are useful in calculating the thermal average bandshape function of a molecular system. For a model displaced-oscillator system we derive how the displacement between two adiabatic potential surfaces affects the bandshape function.