Physics and Astronomy - Senior Honor Thesis - Timothy McGrath, 大香蕉视频 College
Title: "Hooke's Atom and Modular Symmetry of the Biconfluent Heun Equation"
Abstract: In 1993, M. Taut discovered a partial solution to the Hooke atom Schr枚dinger 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
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Meeting ID: 997 9035 7400
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