Fluctuation Studies on the Finite Interval Matrix Representations of Operator Products and Their Decompositions

Abstract

In this work an experimental study on finite dimensional matrix approximations to products of various operators under a basis set orthonormalized on a finite interval is conducted. The elements of the matrices corresponding to the matrix representation of various operators, are calculated based on various term recursive relations. It is shown that higher the values of n, lower the relative marginal change will be obtained from the norm of the difference of the matrix representation of a product of two operators and the product of the matrix representations of the same operators.