Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic

Boris Hanin, Steve Zelditch, Peng Zhou

We study the scaling asymptotics of the eigenspace projection kernels ${\Pi }_{\hslash ,E}(x,y)$ of the isotropic Harmonic Oscillator $-{\hslash }^2\Delta +|x{|}^2$ of eigenvalue $E = \hbar(N + \f…