College of Liberal Arts & Sciences

# Math Physics Seminar

**Abstract:**

I will discuss numerical implementation of the bootstrap method for quantum mechanics. The 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. Continuing the introduction from last week I will show some of the gory details, but move on to focus on numerical implementation of the method for various systems. I will show that the bootstrap effectively reproduces highly non-trivial non-perturbative predictions, shows coherence the semiclassical picture, and reproduces the band structure of periodic potentials. I will comment on algorithmic issues and outlooks for the method.

*(Continuation of David Berenstein's 9/28 talk)*