Category: Numerical Analysis

New Jacobi Polynomials Application January 8, 2024, by James Pate Williams, Jr.

The two primary references used to create my application were: “A Numerical Library in C for Scientists and Engineers” by H. T. Lau and the following website: https://en.wikipedia.org/wiki/Jacobi_polynomials.

Using the Jacobi parameters alpha = 0 and beta = 0, we have the Legendre polynomials for degrees 4 and 6 and their associated roots:

Using alpha = 0.5 and beta= 0.5 we obtain for degrees 4 and 6:

Electron Probability Distribution Function Etc. (c) James Pate Williams, Jr. December 2023

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Some Helium Coulomb Integrals over Six Dimensions by James Pate Williams, Jr. Source Code in C++ Development over December 15 – 16, 2023

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Revised Translated Source Code from May 15, 2015, by James Pate Williams, Jr.

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New and Corrected Ground State Energy Numerical Computation for the Helium Like Atom (Atomic Number 2) by James Pate Williams, Jr.

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A New Calculus of Variations Solution of the Schrödinger Equation for the Lithium Like Atom’s Ground State Energy

This computation took a lot longer time to reach a much better solution than my previously published result.

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A Calculus of Variations Solution to the Quantum Mechanical Schrödinger Wave Equation for the Lithium Like Atom (Atomic Number Z = 3) by James Pate Williams, Jr.

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