Numerical Quantum Mechanics in 3D III

Live Script exploring 2nd-6th-order finite element methods and variable grid density to solve 3D quantum eigenvalue problems.

This educational Live Script shows how to construct 2nd-, 4th-, and 6th-order finite element stencils for a variable grid density with application to the solution to the time-independent Schrodinger equation in three dimensions. The hydrogen atom is used for illustration. The accuracy of such a calculation may be expected to increase with the order at the expense of calculation time. A variable grid allows one to concentrate the function sampling density to match solutions sought, e.g. near the proton when interested in the most tightly bound wave functions.

This script may interest students and instructors in physics, chemistry, and related fields. 'Try this' suggestions, 'Challenges', hyperlinks, and references are included for further exploration. The script expands upon the methods illustrated in Ref[1-2]. Additional educational Live scripts by the author are available at the File Exchange.