Random Matrix theory approach to Quantum mechanics

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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.