A Pleijel-type theorem for the quantum harmonic oscillator
Philippe Charron
TL;DR
This paper establishes a Pleijel-type theorem describing the asymptotic behavior of the number of nodal domains of eigenfunctions of the quantum harmonic oscillator across any dimension.
Contribution
It extends Pleijel's theorem to quantum harmonic oscillators, providing new insights into the nodal domain distribution of their eigenfunctions.
Findings
Asymptotic bounds for nodal domains of quantum harmonic oscillator eigenfunctions
Extension of Pleijel's theorem to higher dimensions
New mathematical framework for analyzing eigenfunction nodal patterns
Abstract
We prove a Pleijel-type theorem for the asymptotic behaviour of the number of nodal domains of eigenfunctions of the quantum harmonic oscillator in any dimension.
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