Nodal Sets of Random Eigenfunctions for the Isotropic Harmonic Oscillator

DOI10.1093/imrn/rnu071zbMath1319.81042arXiv1310.4532OpenAlexW2123485948MaRDI QIDQ5264496

Peng Zhou, Boris Hanin, Steven Zelditch

Publication date: 27 July 2015

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.4532

Mathematics Subject Classification ID

Hamilton's equations (70H05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (10)

Weighted local Weyl laws for elliptic operators ⋮ Nodal sets of Schrödinger eigenfunctions in forbidden regions ⋮ Concentration and universal randomisation of proper subspaces ⋮ Some nodal properties of the quantum harmonic oscillator and other Schrödinger operators in ℝ² ⋮ Scaling of harmonic oscillator eigenfunctions and their nodal sets around the caustic ⋮ Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces ⋮ Interface asymptotics of eigenspace Wigner distributions for the harmonic oscillator ⋮ Semiclassical Cauchy estimates and applications ⋮ Multidimensional Paley-Zygmund theorems and sharp \(L^p\) estimates for some elliptic operators ⋮ Interface asymptotics of Wigner-Weyl distributions for the harmonic oscillator

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