Colloquium

Interface between allowed and forbidden regions

2019.05.22（星期三），10:00-11:00

点：数学院南楼N913

: In classical mechanics, when we talk about a particle of total energy E moving in a potential V,  there is a allowed region {x: E>V(x)} where a particle can freely roam, and a forbidden region {x: E < V(x)} where the particle is not energetic enough to reach. In quantum mechanics, it is also well-known that the wavefunction transitions from fast oscillation to exponential decay. Here we are interested in the question: how does nodal set (zero loci) of the wavefunction change its behavior in these regions? Similarly, for positive hermitian line bundle (L, h) over compact Kahler manifold M, we do analogous study for eigensections for Toeplitz operator acting on L.