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- W4280495589 abstract "The Clebsch–Gordan coefficients are extremely useful in magnetic resonance theory, yet have an infamous perceived level of complexity by many students. The Clebsch–Gordan coefficients are used to determine both the matrix elements of the spherical tensor operators and the total angular momentum states of a system of component angular momenta. Full derivations of these coefficients are rarely worked through step by step. Instead, students are provided with tables accompanied by little or no explanation of where the values in it originated from. This lack of direction is often a source of confusion for students. For this reason, we work through two common examples of the application of the Clebsch–Gordan coefficients to magnetic resonance experiments. In the first, we determine the components of the magnetic resonance Hamiltonian of ranks 0, 1, and 2 and use these to identify the secular portion of the static, heteronuclear dipolar Hamiltonian. In the second, we derive the singlet and triplet states that arise from the interaction of two identical spin- <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mn>1</mn> <mo>/</mo> <mn>2</mn> </math> particles." @default.
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- W4280495589 date "2022-05-17" @default.
- W4280495589 modified "2023-09-30" @default.
- W4280495589 title "The Clebsch–Gordan Coefficients and Their Application to Magnetic Resonance" @default.
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- W4280495589 doi "https://doi.org/10.1155/2022/1143341" @default.
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