Numerical Experimentation to obtain the Laguerre polynomial from average value of all characteristic polynomials of Hermitian Random Matrices

Abstract

Although the behavior of all subatomic particles is inherently probabilistic, Schrodinger´s equation does not itself contain any probabilities. In this work the Authors reinterprets the Schrodinger Equation; to find in it the randomness that was hidden and that was overlooked by Schrodinger himself. From the generation of Hermitian random matrices and their corresponding characteristic polynomials, the Authors concludes that the radial part solution of the Schrodinger equation for the Hydrogen Atom, namely Laguerre Polynomial, is obtained from the average value of all characteristic polynomials. This is how in this work it is made clear that the deterministic method to obtain the Laguerre Polynomial through the Rodrigues Formula is equivalent to the probabilistic method proposed by the Authors.