Nodal sets of random eigenfunctions for the isotropic harmonic oscillator

Boris Hanin; Steve Zelditch; Peng Zhou

doi:10.1093/imrn/rnu071

Nodal sets of random eigenfunctions for the isotropic harmonic oscillator

Boris Hanin, Steve Zelditch, Peng Zhou

Research output: Contribution to journal › Article › peer-review

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Abstract

The expected hypersurface measure H^d-1(Z_E,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) ⊂ℝ^d 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)
Pages (from-to)	4813-4839
Number of pages	27
Journal	International Mathematics Research Notices
Volume	2015
Issue number	13
DOIs	https://doi.org/10.1093/imrn/rnu071
State	Published - 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnu071

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title = "Nodal sets of random eigenfunctions for the isotropic harmonic oscillator",

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.",

author = "Boris Hanin and Steve Zelditch and Peng Zhou",

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AB - 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.

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Nodal sets of random eigenfunctions for the isotropic harmonic oscillator

Abstract

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