Nodal sets of random eigenfunctions for the isotropic harmonic oscillator

Boris Hanin*, Steve Zelditch, Peng Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)4813-4839
Number of pages27
JournalInternational Mathematics Research Notices
Volume2015
Issue number13
DOIs
StatePublished - 2015

ASJC Scopus subject areas

  • Mathematics(all)

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