Spatial Wavefunctions of Spin
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915116491997184 |
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| author | Rakitzis, T. Peter |
| author_facet | Rakitzis, T. Peter |
| contents | We present an alternative formulation of quantum mechanical angular momentum, based on spatial wavefunctions that depend on the Euler angles $ϕ, θ, χ$, and have an additional internal projection $n$. The wavefunctions are Wigner D-functions, $D_{n m}^s (ϕ, θ, χ)$, for which the body-fixed projection quantum number $n$ has the unusual value $n=|s|=\sqrt{s(s+1)}$, or $n=0$. We show that the states $D_{\sqrt{s(s+1)},m}^s (ϕ, θ, χ)$ of elementary particles with spin $\sqrt{s(s+1)}$ give a gyromagnetic ratio of $g=2$ for $s>0$, and we identify these as the spatial angular-momentum wavefunctions of known fundamental charged particles with spin. All known Standard-Model particles can be categorized with either value $n=\sqrt{s(s+1)}$ or $n=0$, and all known particle reactions are consistent with the conservation of its projection in the internal frame, and with internal-frame Clebsch-Gordan coefficients of unity. Therefore, we make the case that the $D_{n m}^s (ϕ, θ, χ)$ are useful as spatial wavefunctions for angular momentum. Some implications and new predictions related to the quantum number $n$ for fundamental particles are discussed, such as the proposed Dirac-fermion nature of the neutrino, the explanation of some Standard-Model structure, and some proposed dark-matter candidates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_13591 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spatial Wavefunctions of Spin Rakitzis, T. Peter Quantum Physics Atomic Physics We present an alternative formulation of quantum mechanical angular momentum, based on spatial wavefunctions that depend on the Euler angles $ϕ, θ, χ$, and have an additional internal projection $n$. The wavefunctions are Wigner D-functions, $D_{n m}^s (ϕ, θ, χ)$, for which the body-fixed projection quantum number $n$ has the unusual value $n=|s|=\sqrt{s(s+1)}$, or $n=0$. We show that the states $D_{\sqrt{s(s+1)},m}^s (ϕ, θ, χ)$ of elementary particles with spin $\sqrt{s(s+1)}$ give a gyromagnetic ratio of $g=2$ for $s>0$, and we identify these as the spatial angular-momentum wavefunctions of known fundamental charged particles with spin. All known Standard-Model particles can be categorized with either value $n=\sqrt{s(s+1)}$ or $n=0$, and all known particle reactions are consistent with the conservation of its projection in the internal frame, and with internal-frame Clebsch-Gordan coefficients of unity. Therefore, we make the case that the $D_{n m}^s (ϕ, θ, χ)$ are useful as spatial wavefunctions for angular momentum. Some implications and new predictions related to the quantum number $n$ for fundamental particles are discussed, such as the proposed Dirac-fermion nature of the neutrino, the explanation of some Standard-Model structure, and some proposed dark-matter candidates. |
| title | Spatial Wavefunctions of Spin |
| topic | Quantum Physics Atomic Physics |
| url | https://arxiv.org/abs/2307.13591 |