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

By Alan J. Benesi

Provides the speculation of NMR stronger with Mathematica© notebooks

  • Provides brief, targeted chapters with short factors of well-defined issues 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 type of textual content, images, sound, and calculations
  • Based on category confirmed equipment built by means of the writer over his 25 12 months instructing profession. those notebooks express precisely how the idea works and supply important calculation templates for NMR researchers

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

Sample text

33 34 A Primer of NMR Theory with calculations in Mathematica® absorptive component and a dispersive imaginary component. 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”).

1 except that the net magnetization after the (π/2)ϕ rf pulse is at +ϕ radians relative to the –y axis. Do not confuse the magnetization vector (thicker arrow) with the B1 vector (thinner arrow) located at ϕ radians relative to the +x axis. 4 shows the vector model for a single off‐resonance (δ ≠ 0) 90° pulse along the x axis of the rotating frame. In this case, after the (π/2)x rf pulse, the ­magnetization precesses in the x–y plane around the z axis at δ radians s−1. Relaxation components are not depicted.

T2 relaxation during the two τ delays reduces the magnitude of M in the xy plane, but the magnetization is otherwise unaffected. The experiment is repeated for different τ values, yielding data that can be analyzed to measure the T2 value. Failure of vector model for J-coupling, showing the on-resonance spin magnetization only z –x M y After (π/2)y τ +2 π (J/2)τ x –y –2 π (J/2)τ –z Observed: signal disappears! 7 Failure of the Vector Model for Two J‐coupled I = 1/2 Nuclear Spins. One spin is on‐resonance (δ = 0) and one is off‐resonance (δ ≠ 0).

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