What Physicists Do Lecture Series: Solving Quantum Mechanics with Positivity

Presenter Full Name: David Berenstein
Institution: UCSB

I will describe some recent results for solving certain quantum mechanical systems within the "Bootstrap" approach. The two main ideas are that integrals of positive functions are positive and that in many 1-D quantum systems there are recursion relations that let one evaluate a lot of such integrals from very little extra data. Surprisingly, these positive inequalities let one zero in on the energy levels exactly, by excluding regions of data. I will also talk about how to optimize the finding of valid regions.