Utilizing Supersymmetry to Calculate Partner Potential Eigenfunctions of the Infinite Square Well
As a final project for my Computational Physics class, I will create a poster containing the results of the algorithm related to the field of quantum mechanics that I will have created as a final product. The project consists in creating a Python algorithm that calculates and plots various “eigenfunctions” of a potential function known as the “infinite square well” utilizing the concept of supersymmetry. Supersymmetry (SUSY) is a physical theory that relates mass and energy and has served to make advancements towards a unified theory of the universe. In the field of quantum mechanics, SUSY has been utilized to factorize the Schrodinger equation with the purpose of solving basic quantum mechanical models, such as the harmonic oscillator. With the infinite square well, SUSY has served to obtain new solvable partner potentials with their corresponding eigenenergies and eigenfunctions using raising and lowering operators. The goal of my final algorithm is to numerically calculate several partner potential wells of the infinite square well with their corresponding eigenfunctions and eigenenergies. The output of the final code will contain a plot of all the partner potentials with the first three or four eigenfunctions corresponding to each potential well (even though the code will be able to calculate much more eigenfunctions for each well). The poster will include the theoretical framework of how SUSY works on the infinite square well, the details of how the code calculates new potential wells with plots of the various eigenfunctions, and the output of the algorithm.