{"title":"Density Matrix of Two Spin-1/2 Particles: Pure and Mixed States","authors":"Eric R. Johnston","doi":"10.1155/2024/9907579","DOIUrl":null,"url":null,"abstract":"<div>\n <p>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.</p>\n </div>","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2024 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2024/9907579","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concepts in Magnetic Resonance Part A","FirstCategoryId":"92","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1155/2024/9907579","RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
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Abstract
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.
期刊介绍：
Concepts in Magnetic Resonance Part A brings together clinicians, chemists, and physicists involved in the application of magnetic resonance techniques. The journal welcomes contributions predominantly from the fields of magnetic resonance imaging (MRI), nuclear magnetic resonance (NMR), and electron paramagnetic resonance (EPR), but also encourages submissions relating to less common magnetic resonance imaging and analytical methods.
Contributors come from academic, governmental, and clinical communities, to disseminate the latest important experimental results from medical, non-medical, and analytical magnetic resonance methods, as well as related computational and theoretical advances.
Subject areas include (but are by no means limited to):
-Fundamental advances in the understanding of magnetic resonance
-Experimental results from magnetic resonance imaging (including MRI and its specialized applications)
-Experimental results from magnetic resonance spectroscopy (including NMR, EPR, and their specialized applications)
-Computational and theoretical support and prediction for experimental results
-Focused reviews providing commentary and discussion on recent results and developments in topical areas of investigation
-Reviews of magnetic resonance approaches with a tutorial or educational approach
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