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arXiv · 2512.07347

Self-adjoint realization of the harmonic oscillator in polar coordinates and some consequences

Krzysztof Stempak
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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.

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Krzysztof Stempak. 2025-12-08. Self-adjoint realization of the harmonic oscillator in polar coordinates and some consequences. https://arxiv.org/abs/2512.07347

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