MATHEMATICS COLLOQUIUM
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Speaker: Dr. Eyal Subag, Pennsylvania State University
Title: The algebraic symmetry of the hydrogen atom
Date & Time: Tuesday, January 21, 2020, at 13:00
Place: Room EM204, ORT Braude College, Karmiel
Abstract
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I will describe a new type of algebraic symmetry for the system. I will show that the collection of all regular solutions of the Schrödinger equation is an algebraic family of representations of different algebras. Such a family is known as an algebraic family of Harish-Chandra modules. The algebraic family has a canonical filtration from which the physically relevant solutions and the spectrum of the Schrödinger operator can be recovered.
If time permits I will relate the spectral theory of the Schrödinger operator to the algebraic family. No prior knowledge about quantum mechanics or representation theory will be assumed.