Exponential operators, generalized polynomials and evolution problems

The operator (d/ds)chid/dx plays a central role in the theory of operationa l calculus. Its exponential form is crucial in problems relevant to solutio ns of Fokker-Planck and Schrodinger equations. We explore the formal proper ties of the evolution operators associated to (d/dx)chid/dx, discuss its li nk to special forms of Laguerre polynomials and Laguerre-based functions. T he obtained results are finally applied to specific problems concerning the solution of Fokker-Planck equations relevant to the beam lifetime in stora ge rings. (C) 2001 Elsevier Science Ltd. All rights reserved.