Spectral Theory for the Laplacian by Abby Kinney '24

Spectral Theory for the Laplacian by Abby Kinney ’24, Wednesday April 24, 1:00 – 1:50pm, North Science Building 113, Wachenheim

Abstract: In quantum mechanics, physicists seek to understand observable quantities. Spectral theory provides us with the mathematical structure to understand these physical quantities in terms of operators in Hilbert space. We will define the spectrum of an operator and determine the spectrum of the Laplacian. With this result, we will explore the spectrum of a time-independent two-body Schrödinger operator and state an upper limit on the number of bound states.