Applying classical geometry intuition to quantum spin
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Publication:2835948
DOI10.1088/0143-0807/37/5/055409zbMATH Open1349.81113arXiv1201.0302OpenAlexW2964316608MaRDI QIDQ2835948
Author name not available (Why is that?)
Publication date: 30 November 2016
Published in: (Search for Journal in Brave)
Abstract: Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a mathematically rigorous derivation, the relationships are found by forcing expectation values of the different basis states to have the properties we expect of a classical, geometric coordinate system. The process highlights the correspondence of quantum angular momentum with classical notions of geometric orthogonality, even for the inherently non-classical spin-1/2 system. In the process, differences in and connections between geometrical space and Hilbert space are illustrated.
Full work available at URL: https://arxiv.org/abs/1201.0302
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