By Alan J. Benesi
Offers the speculation of NMR improved with Mathematica© notebooks
- Provides brief, concentrated chapters with short motives of well-defined subject matters 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, snap shots, sound, and calculations
- Based on category proven equipment built by way 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 resources for A Primer of NMR Theory with Calculations in Mathematica
This transformation does not affect ρeq. In contrast, the next cells show that rotations around the x or y axes transform ρeq to forms with non‐zero x and y components. We then show that these transverse components (coherences) arise from only the difference term b. The next cells show explicitly that the constant term is unaffected by rotations about any axis and cannot generate off‐diagonal coherence. 6, is significantly transformed by rotations around the x and y axes. The final cell, a comment, is worth repeating.
The resulting dMdt vector contains x, y, and z components, respectively. These can be easily extracted as shown in the following cells. The next cells show how DSolve is used to solve the Bloch equation for the time dependence of the magnetization M given that it is initially on the +x axis (as it would be after a 90° +y rf pulse). See Chapter 5 for the introduction of DSolve. Note how the x, y, and z components of dMdt are used to achieve the solution. The desired solutions Mx[t], My[t], and Mz[t] are also identified as is the independent time variable t.
0 × 10−5 s in increments of 1 × 10−6 s. The animations that greater offsets (δ) reduce the efficiency of rf pulses. nb This notebook is similar to the previous one, except that this looks at the net magnetization in the rotating frame after “hard” rf pulses (ω1 >> δ). The initial position of the net magnetization after a hard pulse is defined by θ = ω1 τpulse, where τpulse is the duration of the pulse in s, and by ϕ, the phase of the pulse in the rotating frame. The initial x, y, and z magnetization components are given by Sin[θ] Sin[ϕ], −Sin[θ] Sin[ϕ], and Cos[θ], respectively for Mzeq = 1.
A Primer of NMR Theory with Calculations in Mathematica by Alan J. Benesi