Open AccessNumerical Experimentation to obtain the Laguerre polynomial from average value of all characteristic polynomials of Hermitian Random Matrices
Author(s) -
Mr. Gonzalez,
H. E.,
L. Carmona,
J. J.
Publication year - 2021
Publication title -
international journal of engineering and innovative technology
Language(s) - English
Resource type - Journals
ISSN - 2277-3754
DOI - 10.51456/ijeit.2021.v11i03.001
Subject(s) - laguerre polynomials , hermitian matrix , mathematics , schrödinger equation , randomness , laguerre's method , polynomial , orthogonal polynomials , random variate , mathematical analysis , classical orthogonal polynomials , pure mathematics , random variable , statistics
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.