Comments on operational methods and diffusion problems

Laguerre-type PDE problems are related to the so called Laguerre derivative ĎL := Dx xDx which appears when studying diffusion problems and even in mechanical problems such as the oscillating chain. In this article we use an operational approach in order to write down explicitly the solutions of problems depending on analytical initial or boundary data. Further applications to the Schrӧdinger equation and other diffusion problems are considered in the last section.