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Strong quantum zero-point motion (ZPM) of light nuclei and other particles is a crucial aspect of many state-of-the-art quantum materials. However, it has only recently begun to be explored from an ab initio perspective, through several competing approximations. Here we develop a unified description of muon and light nucleus ZPM and establish the regimes of anharmonicity and positional quantum entanglement where different approximation schemes apply. Via density functional theory and path-integral molecular dynamics simulations we demonstrate that in solid nitrogen,
α
–N
2
, muon ZPM is both strongly anharmonic and many-body in character, with the muon forming an extended electric-dipole polaron around a central, quantum-entangled [N
2
–
μ
–N
2
]
+
complex. By combining this quantitative description of quantum muon ZPM with precision muon quadrupolar level-crossing resonance experiments, we independently determine the static
14
N nuclear quadrupolar coupling constant of pristine
α
–N
2
to be –5.36(2) MHz, a significant improvement in accuracy over the previously-accepted value of –5.39(5) MHz, and a validation of our unified description of light-particle ZPM.
Quantum entanglement and uncertainty in the positions of light nuclei and implanted particles can crucially impact our understanding of advanced materials. This paper develops a unified theoretical description of these effects and applies it to muon spectroscopy measurements of a material constant to significantly improve their accuracy.