Self-adjoint realization of the harmonic oscillator in polar coordinates and some consequences
Year: 2025
Type: preprint
Abstract: We consider spectral decomposition of the harmonic oscillator in $\mathbb R^n$ in terms of two different orthonormal bases in $L^2(\mathbb R^n)$ consisting of its eigenfunctions. Then, using purely functional analysis tools we provide simple proofs of rotational symmetry of the Hermite projection operators studied by Kochneff, and Thangavelu's Hecke-Bochner type identity.
Source: arXiv (Cornell University)
Author: Stempak, Krzysztof
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7110841632
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