IJAM, Volume 26, No. 5 (2013)

Abstract. Several authors [1, 2, 3, 4, 5, 6] have found some types of non classical orthogonal polynomials, called as Exceptional orthogonal polynomials (EOP), while solving some quantum mechanical systems. Especially, it is Quesne [8, 9] who first observed the presence of a relationship between the exceptional orthogonal polynomials, the Darboux transformation and the shape invariant potentials in quantum mechanics. In this article we demonstrate explicitly the completeness property (in weighted space) of Exceptional orthogonal polynomials (EOP) [2] in connection with the quantum mechanical states of some categories of well-known quantum mechanical systems.