Self-adjoint realization of the harmonic oscillator in polar coordinates and some consequences
Functional Analysis
2025-12-09 v1
Abstract
We consider spectral decomposition of the harmonic oscillator in in terms of two different orthonormal bases in 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.
Keywords
Cite
@article{arxiv.2512.07347,
title = {Self-adjoint realization of the harmonic oscillator in polar coordinates and some consequences},
author = {Krzysztof Stempak},
journal= {arXiv preprint arXiv:2512.07347},
year = {2025}
}