Density Matrix of Two Spin‐1/2 Particles: Pure and Mixed States

The density matrix of an arbitrary pure state of a system consisting of two spin‐1/2 particles is derived from the Pauli spin angular momentum operators. Mixed singlet and triplet states are then formed from linear combinations of pure states and their corresponding density matrices constructed. Sin...

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Bibliographic Details
Published in:Concepts in magnetic resonance. Part A, Bridging education and research Bridging education and research, 2024-01, Vol.2024 (1)
Main Author: Johnston, Eric R.
Format: Article
Language:English
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Summary:The density matrix of an arbitrary pure state of a system consisting of two spin‐1/2 particles is derived from the Pauli spin angular momentum operators. Mixed singlet and triplet states are then formed from linear combinations of pure states and their corresponding density matrices constructed. Singlet and triplet states are exemplified by the spin isomers parahydrogen and orthohydrogen, respectively. Partial mixing is illustrated with the example of bilinear spin–spin coupling. Various properties of the density matrices of pure and mixed states are discussed, including idempotence, factoring, and spin correlation.
ISSN:1546-6086
1552-5023
DOI:10.1155/2024/9907579