Computational applications in physics: Spectral representation of Green’s function with Python

This article explores the use of the Sturm-Liouville operator in the spectral representation of the Green’s function, highlighting its applicability in mathematical physics. We focus on spectral representation as a technique for solving non-homogeneous differential equations, using the eigenfunctions of the Sturm-Liouville operator. We demonstrate the application of these concepts in fundamental problems of electromagnetism, and quantum mechanics, obtaining analytical solutions and revisiting concepts. We highlight the use of Python programming for the graphical visualization of solutions, facilitating the understanding of complex mathematical concepts and offering an intuitive approach to the analysis of physical phenomena. In the final section, we emphasize how the work provides valuable insights for the solution of differential equations and the interpretation of physical phenomena. We conclude by pointing to future work, suggesting an even deeper integration between programming and mathematics in contemporary physics, with the goal of making learning more intuitive.

Keywords:
Sturm-Liouville Operator; Green Funcion; Python Programming