Uniform bounds, zero separation and monotonicity for the regular Coulomb wave functions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913518506213376 |
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| author | Chung, Seok-Young |
| author_facet | Chung, Seok-Young |
| contents | This paper begins by deriving the uniform bounds for the regular Coulomb wave function $F_{\ell,η}$ and its derivative $F_{\ell,η}'$. We then examine detailed zero configurations of $F_{\ell,η}$ and $F_{\ell+1,η}$, extending insights into the earlier work that was restricted to $\ell>-3/2$. Our investigation also includes an analysis of the monotonicity of the zeros of $F_{\ell,η}$ with respect to parameters $\ell$ and $η$, respectively. Furthermore, we expand our exploration to associated orthogonal polynomials, as well as the functions involving both $F_{\ell,η}$ and $F_{\ell,η}'$. Finally, we explore the breakdown of the Sturm separation theorem by means of the zeros of associated orthogonal polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform bounds, zero separation and monotonicity for the regular Coulomb wave functions Chung, Seok-Young Classical Analysis and ODEs 33C45, 30C15, 34C10 This paper begins by deriving the uniform bounds for the regular Coulomb wave function $F_{\ell,η}$ and its derivative $F_{\ell,η}'$. We then examine detailed zero configurations of $F_{\ell,η}$ and $F_{\ell+1,η}$, extending insights into the earlier work that was restricted to $\ell>-3/2$. Our investigation also includes an analysis of the monotonicity of the zeros of $F_{\ell,η}$ with respect to parameters $\ell$ and $η$, respectively. Furthermore, we expand our exploration to associated orthogonal polynomials, as well as the functions involving both $F_{\ell,η}$ and $F_{\ell,η}'$. Finally, we explore the breakdown of the Sturm separation theorem by means of the zeros of associated orthogonal polynomials. |
| title | Uniform bounds, zero separation and monotonicity for the regular Coulomb wave functions |
| topic | Classical Analysis and ODEs 33C45, 30C15, 34C10 |
| url | https://arxiv.org/abs/2409.17305 |