The operator (d/dx)Χd/dx plays a central role in the theory of operational calculus. Its exponential form is crucial in problems relevant to solutions of Fokker-Planck and Schrödinger equations. We explore the formal properties of the evolution operators associated to (d/dx)Χd/dx, discuss its link to special forms of Laguerre polynomials and Laguerre-based functions. The obtained results are finally applied to specific problems concerning the solution of Fokker-Planck equations relevant to the beam lifetime in storage rings. © 2001 Elsevier Science Ltd.
All Science Journal Classification (ASJC) codes
Dattoli, G., Mancho, A. M., Quattromini, M., & Torre, A. (2001). Exponential operators, generalized polynomials and evolution problems. Radiation Physics and Chemistry, 61(2), 99 - 108. https://doi.org/10.1016/S0969-806X(00)00426-6