Math Physics Seminar

Speaker: 
Prof. David Berenstein, UCSB
Topic: 
Bootstrapping Quantum mechanical systems in 1D

Abstract:

I will show how one can solve numerically for the energy levels of certain quantum mechanical systems using a recursive plus unitarity method.  This method, called "bootstrap", uses the equations of motion of the system to find recursions between certain expectation values in an energy eigenstate.  Combined with positivity of the expectation value of any positive operator (what one calls unitarity), one finds relations to classic problems in mathematics: the moment problem.  One can check this positivity numerically and theorems guarantee the existence of a probability measure that solves the moment problem if certain conditions are satisfied.

Event Date: 
September 28, 2021 - 2:30pm to 3:20pm
Location: 
VAN 309 or Online (See URL)
Calendar Category: 
Seminar
Seminar Category: 
Mathematical Physics