The expected hypersurface measure Hd-1(ZE,h ∩ B(r, x)) of nodal sets of random eigen-functions of eigenvalue E of the semiclassical isotropic harmonic oscillator in balls B(r, x) ⊂ℝd is determined as h→0. In the allowed region the volumes are of order h-1, while in the forbidden region they are of order h-1/2.
|Original language||English (US)|
|Number of pages||27|
|Journal||International Mathematics Research Notices|
|State||Published - 2015|
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