Download PDF by Alan J. Benesi: A Primer of NMR Theory with Calculations in Mathematica

By Alan J. Benesi

ISBN-10: 1118588991

ISBN-13: 9781118588994

Provides the speculation of NMR more advantageous with Mathematica© notebooks

  • Provides brief, centred chapters with short reasons of well-defined themes with an emphasis on a mathematical description
  • Presents crucial effects from quantum mechanics concisely and for simple use in predicting and simulating the result of NMR experiments
  • Includes Mathematica notebooks that enforce the speculation within the kind of textual content, pictures, sound, and calculations
  • Based on category confirmed equipment constructed through the writer over his 25 12 months instructing occupation. those notebooks express precisely how the speculation works and supply worthy calculation templates for NMR researchers

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Additional resources for A Primer of NMR Theory with Calculations in Mathematica

Example text

Random, incoherent off‐ diagonal elements can also be created by thermal fluctuations of the internal Hamiltonians. 3) k A Primer of NMR Theory with Calculations in Mathematica®, First Edition. Alan J. Benesi. © 2015 John Wiley & Sons, Inc. Published 2015 by John Wiley & Sons, Inc. 4) of the spin angular momentum operator Î+. Ch a p te r 13 The Liouville–von Neumann Equation The Liouville–von Neumann equation (von Neumann, 1932) is the equation of motion for the density operator. It applies to the density operator of a single nuclear spin and to the density operator for an ensemble of spins.

Therefore, it cannot be used to generate off‐diagonal coherence observable in NMR experiments and can be ignored. Only the difference in population between Zeeman levels can give rise to off‐diagonal coherence. 5b) k where bk = ħω0k/kBT. nb, transforming from the laboratory to the rotating frame does not change the equilibrium density matrix. 5. This result is of extreme importance because it is the starting point for all NMR experiments. ˆ eq is the only part of the ensemble density operator that can be changed by the Liouville–von Neumann equation (Eqs.

These are converted, respectively, into an absorption function and a dispersion function in the next cells. The built‐in Mathematica function Plot is used to plot the absorption and dispersion spectra for the parameters a = 1, T2 = 1 s−1, δ = 0 radian s−1. It is shown that identical results are obtained for the same parameters if the spectrum is left in the original imaginary form (see Plots of the function “spec”). Next, the built‐in Mathematica function FindRoot is used to find the peak width at half height of the absorption spectrum.

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A Primer of NMR Theory with Calculations in Mathematica by Alan J. Benesi

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