A study of random variables in terms of the number operator

Abstract

We show first how the joint semi-quantum and quantum operators of a finite family of random variables having finite moments of all orders can be recovered from their joint number operator. We then characterize the polynomially symmetric and polynomially factorizable random variables in terms of their joint number operator. Finally, we present the quantum decomposition of the number and quantum operators of the random variables whose orthogonal polynomials are the Gegenbauer polynomials.