A Spectral Gap Estimate and Applications

Bogdan Georgiev, Mayukh Mukherjee, Stefan Steinerberger

We consider the Schrödinger operator $$-\frac{d^2}{d x^2} + V \qquad \mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions},$$ where $V$ is bounded from below and p…