Research Assistance
The Pennsylvania State University
Atomic Orbitals
October 2019 - March 2020
This is a mathematical, derivation-based research project for my introductory physics professor. I calculated and derived several quantum mechanical equations.
Background
This project attempted to answer the question asked by a layperson on the subject: “What are atomic energy levels and orbitals, and why do atoms have them?”
Dr. Tussey, my Fall 2019 Physics professor, wondered how we should respond to such a question:
- Should we attempt a basic conceptual approach, speaking of standing waves, etc., or a more rigorous mathematical approach? Most laypersons may not have the mathematical sophistication to understand a mathematical answer.
- How satisfying would a direct answer be to someone who knows nothing about atoms?
- After doing a detailed derivation, can we find a simple way of communicating the answer that is understandable by anyone?
- What will it take to satisfactorily answer this question?
To approach this, we had to first consider:
- Has anyone already answered this question? If so, who?
- What is out there in the scientific literature?
- What is the common answer to the question?
- What is out there (YouTube etc.) in terms of explanations?
- Why are we attempting to answer this question?
To complete the project, we had to derive the wave equation for a photon using Maxwell’s equations, use the Planck/Einstein photon concept to derive the Klein-Gordon (KG) equation, derive the time-dependent Schrodinger equation (TDSE) for the non-relativistic case (Taylor expand the energy keeping only the dominant terms), and solve the TDSE for the H atom.
My Involvement
My friend Kade and I were in charge of calculating the first two steps of the process: The Wave Equation and The Schrödinger Equation. Using Maxwell’s equations, we derived The Wave Equation. We additionally used The Wave Equation to derive The Schrödinger Equation.
However, due to department understaffing and the Covid-19 pandemic, that is as far as we have gotten with the project.