Related papers: Spatial Wavefunctions of Spin

Spatial Wavefunctions of Spin

URL: http://arxiv.org/abs/2307.13591v6
Date: Tue, 22 Oct 2024 17:40:10 GMT
Title: Spatial Wavefunctions of Spin
Authors: T. Peter Rakitzis,
Abstract summary: We present an alternative formulation of quantum mechanical angular momentum. The wavefunctions are Wigner D-functions, $D_n ms (phi, theta, chi)$. Some implications of the quantum number $n$ for fundamental particles are discussed.
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Abstract: We present an alternative formulation of quantum mechanical angular momentum, based on spatial wavefunctions that depend on the Euler angles $\phi, \theta, \chi$. The wavefunctions are Wigner D-functions, $D_{n m}^s (\phi, \theta, \chi)$, for which the body-fixed projection quantum number $n$ has the unusual value $n=|s|=\sqrt{s(s+1)}$, or $n=0$. The $D_{\sqrt{s(s+1)},m}^s (\phi, \theta, \chi)$ wavefunctions are unnormalizable, however we demonstrate a regularization procedure that allows the calculation of expectation values: for example, the states $D_{\sqrt{s(s+1)} m}^s (\phi, \theta, \chi)$ of elementary particles with spin $s$ 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. Therefore, we make the case that the $D_{n m}^s (\phi, \theta, \chi)$ are useful as spatial wavefunctions for angular momentum. Some implications of the quantum number $n$ for fundamental particles are discussed, such as the proposed Dirac-fermion nature of the neutrino, and some proposed dark-matter candidates.

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