The quantum and semi-quantum operators, generated by a probability measure having finite moments of all orders, are presented first. We continue by giving a general proposition about writing these operators as a sum of products (compositions) of multiplication by X and differentiation, D operators, in which all the X factors are to the left of the D factors. We show some concrete computations, of the semi-quantum operators, for the random variables that belong to the Meixner class. Finally, we show how these computations can be used to recover all the distributions from the Meixner class.
427 Thackeray Hall