  In this paper, we give random matrix theory approach to the quantum mechanics
using the quantum Hamilton-Jacobi formalism. We show that the bound state
problems in quantum mechanics are analogous to solving Gaussian unitary
ensemble of random matrix theory. This study helps in identify the potential
appear in the joint probability distribution function in the random matrix
theory as a super potential. This approach allows to extend the random matrix
theory to the newly discovered exceptional polynomials.
