%0 Journal Article
%T Nodal Sets of Random Eigenfunctions for the Isotropic Harmonic Oscillator
%A Boris Hanin
%A Steve Zelditch
%A Peng Zhou
%J Mathematics
%D 2013
%I arXiv
%X We consider Gaussian random eigenfunctions (Hermite functions) of fixed energy level of the isotropic semi-classical Harmonic Oscillator on ${\bf R}^n$. We calculate the expected density of zeros of a random eigenfunction in the semi-classical limit $h \to 0.$ In the allowed region the density is of order $h^{-1},$ while in the forbidden region the density is of order $h^{-\frac{1}{2}}$. The computer graphics due to E.J. Heller illustrate this difference in "frequency" between the allowed and forbidden nodal sets.
%U http://arxiv.org/abs/1310.4532v2