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Full-Text Articles in Physical Sciences and Mathematics
The Global Stability Of The Solution To The Morse Potential In A Catastrophic Regime, Weerapat Pittayakanchit
The Global Stability Of The Solution To The Morse Potential In A Catastrophic Regime, Weerapat Pittayakanchit
HMC Senior Theses
Swarms of animals exhibit aggregations whose behavior is a challenge for mathematicians to understand. We analyze this behavior numerically and analytically by using the pairwise interaction model known as the Morse potential. Our goal is to prove the global stability of the candidate local minimizer in 1D found in A Primer of Swarm Equilibria. Using the calculus of variations and eigenvalues analysis, we conclude that the candidate local minimizer is a global minimum with respect to all solution smaller than its support. In addition, we manage to extend the global stability condition to any solutions whose support has a single …
The Pekeris Method For Lithium: Possibilities And Obstructions, Marcel Kreuter
The Pekeris Method For Lithium: Possibilities And Obstructions, Marcel Kreuter
Theses and Dissertations
It is widely believed that the properties of atoms and molecules are accurately described by the Schrödinger equation, at least in so far as relativistic effects may be neglected. Extracting these properties from the equation in practice, however, can be a highly challenging task. In 1958, Chaim L. Pekeris developed a method for computing the ground state energy of the Helium atom. This thesis surveys the possibilities and obstructions that occur when one tries to compute the ground state energy of Lithium using Pekeris's method.