Approximating the Ground State Eigenvalue via the Landscape Potential

Abstract: In this talk, we study the ground state energy of a Schroedinger operator and its relation to the landscape potential. For the 1-d Bernoulli Anderson model, we show that the ratio of the ground state energy and the minimum of the landscape potential approaches $\pi^2/8$ as the domain size approaches infinity. We then discuss some numerical stimulations and conjectures for excited states and for other random potentials. The talk is based on joint work with I. Chenn and W. Wang.

MathematicsPhysics

Audience: researchers in the topic

UCI Mathematical Physics