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Physics and Astronomy - Senior Honor Thesis - Timothy McGrath, Dartmouth College

Title: "Hooke's Atom and Modular Symmetry of the Biconfluent Heun Equation"

6/4/2025
4 pm – 6 pm
Wilder 202 and Zoom
Intended Audience(s): Public
Categories: Arts and Sciences, Lectures & Seminars

Abstract: In 1993, M. Taut discovered a partial solution to the Hooke atom Schrödinger equation: a spectrum of eigenvalues and corresponding eigenfunctions which solve the equation, but which are valid only for a particular set of discrete values of the harmonic oscillator frequency. This phenomenon occurs in certain ordinary, one-dimensional differential equations and is commonly referred to as quasi-solvability. This project will investigate the modular invariance/quasi-solvability of the Hooke atom, through semi-analytical methods such as canonical transformations and numerical approximations. Our goal is to provide a more general form of the solution, and to better understand why quasi-solvability occurs for the Hooke atom potential and other potential energy functions. 

 

Advisor: Rufus Boyack

Join Zoom Meeting
https://dartmouth.zoom.us/j/99790357400?pwd=EurfQrp4wPehDbRYNM79hLFlzXV062.1

Meeting ID: 997 9035 7400
Email Physics.Department@dartmouth.edu for passcode

For more information, contact:
Tressena Manning
tressena.a.manning@dartmouth.edu
603-646-2854
Permanent URL to this event: https://physics.dartmouth.edu/events/event?event=78064

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