Category: Schrödinger Equation

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

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More than Four Dimensions Why Worry a Blog Entry by James Pate Williams, Jr. December 27, 2023

Some modern physical models of our universe require more than Einstein’s four dimensions: three spatial dimensions and one time dimension. Why do people worry about introducing more dimensions into our understanding of chemistry and physics? When Erwin Schrödinger introduced his famous quantum mechanical two-body solution of the time independent hydrogen-like atom wave equation he went four dimensions to three spatial dimensions. Later, Wolfgang Pauli espoused his famous Pauli Exclusion Principle that simply stated no two electrons (fermions) in an atomic orbital can have the same quantum spin number. Atoms live in a four-dimensional quantum number space augmented by three spatial dimensions and one time dimension.

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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Win32 C Orthogonal Polynomials

I learned about the Laguerre and Legendre polynomials when I first read “Introduction to Quantum Mechanics” by Pauling and Wilson way back in the early 1970s. I later learned about the Chebyshev and other orthogonal polynomials. Beginning on March 30, 2015, I created yet another application to graph various orthogonal polynomials in C#. A few days ago, I wrote a Win32 C application to graph the Chebyshev, Laguerre, and Legendre orthogonal polynomials. At a later date, I will probably add Hermite and Jacobi polynomials.