Our final seminar talk of the fall 2025 semester will be given by José Garcia on December 12. Please join us!

Title: Approximate position localized states in the Schrödinger picture

Abstract: Solutions to the Schrödinger equation boil down to computing the eigenstates of the corresponding Hamiltonian operator. These eigenstates are not only the standing or stationary solutions, but they also determine the time evolution operator for the state. In applications it is sometimes ideal to have standing states that are also localized in position. Having an eigenstate that is localized in position is almost never the case. The best we can do is find states that are approximately localized in position that are also approximate eigenstates of the Hamiltonian. To do this we will talk about the Quadratic e-pseudospectrum, it’s properties and how it can help us attempt at answering the question of how to find approximate eigenstates that are approximately localize in position. The aim of the talk is to give an overview of methods being studied and all are welcome to attend, applied mathematicians, theoretical mathematicians, and overall people in the sciences.