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

IF 0.4 4区化学 Q4 CHEMISTRY, PHYSICAL

Concepts in Magnetic Resonance Part A Pub Date : 2024-11-14 DOI:10.1155/2024/9907579

Eric R. Johnston

引用次数: 0

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.

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两个自旋-1/2 粒子的密度矩阵：纯态和混合态

由两个自旋-1/2 粒子组成的系统的任意纯态的密度矩阵是由保利自旋角动量算子推导出来的。混合单重态和三重态则由纯态的线性组合形成，并构建相应的密度矩阵。单重态和三重态分别以自旋异构体对氢和正氢为例。部分混合以双线性自旋-自旋耦合为例进行说明。讨论了纯态和混合态密度矩阵的各种特性，包括幂等性、因子和自旋相关性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Concepts in Magnetic Resonance Part A 物理-光谱学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

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