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Modern Physics Letters A

Angular momentum and NMR: A brief note

G. S. Burra

Published Feb 28, 2023• 0 citations
Publisher

Abstract

Using noncommutative infinitesimal rotations, we work out a formulation for angular momentum which leads to an expression for nuclear magnetic resonance (NMR). We also indicate a cosmic footprint of these considerations, much like the 21 cm radio signal of cosmic Hydrogen. Here, the motivation is that there are a number of “second-order effects” which provide results over and above the usual well-known results.

DOI
10.1142/s0217732323500402

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Using noncommutative infinitesimal rotations, we work out a formulation for angular momentum which leads to an expression for nuclear magnetic resonance (NMR). We also indicate a cosmic footprint of these considerations, much like the 21 cm radio signal of cosmic Hydrogen. Here, the motivation is that there are a number of “second-order effects” which provide results over and above the usual well-known results.
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Synopsis: General operator properties of angular momenta are recalled, and a physical motivation for adding them is given. ƒe product and total angular momentum bases are defined. It is shown how to express one basis in terms of the other, and an explicit example of adding two spin 1/2 angular momenta is given. A further example consists of adding a general orbital angular momentum value to spin 1/2. ƒese considerations are applied to perturbations in the hydrogen atom energy spectrum, where the correct choice for calculations is the total angular momentum basis.
Angular momentum is essential to any advanced discussion of magnetic resonance spectroscopy. A brief history of the modern sub-atomic particle-spin concept is presented. The origin of the spin-1/2 angular momentum quantum number is detailed and angular momentum operators are constructed for spin-1/2 nuclei using the postulates of quantum mechanics that are then used to produce a set of very useful eigenvalue formulas. Angular momentum operators in spherical coordinate form are developed and operator matrices are constructed from Cartesian operators. The time-evolution of these operators is of much interest in later chapters and is explored in some detail here.
Angular momentum is essential to any advanced discussion of magnetic resonance spectroscopy. A brief history of the modern sub-atomic particle-spin concept is presented. The origin of the spin-1/2 angular momentum quantum number is detailed and angular momentum operators are constructed for spin-1/2 nuclei using the postulates of quantum mechanics which are then used to produce a set of very useful eigenvalue formulas. Angular momentum operators in spherical coordinate form are developed and operator matrices are constructed from Cartesian operators. The time-evolution of these operators is of much interest in later chapters and is explored in some detail here.