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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2512.07347 |
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| _version_ | 1866909949195452416 |
|---|---|
| author | Stempak, Krzysztof |
| author_facet | Stempak, Krzysztof |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07347 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-adjoint realization of the harmonic oscillator in polar coordinates and some consequences Stempak, Krzysztof Functional Analysis 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. |
| title | Self-adjoint realization of the harmonic oscillator in polar coordinates and some consequences |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2512.07347 |