By Alan J. Benesi
Provides the idea of NMR better with Mathematica© notebooks
- Provides brief, concentrated chapters with short motives 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 idea within the type of textual content, photos, sound, and calculations
- Based on classification established tools constructed via the writer over his 25 12 months educating profession. those notebooks express precisely how the speculation works and supply worthwhile calculation templates for NMR researchers
Read or Download A Primer of NMR Theory with Calculations in Mathematica PDF
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Extra info for A Primer of NMR Theory with Calculations in Mathematica
A are demonstrated. Matrix multiplication of square matrices yields a square matrix of the same dimensionality, in this case 3 × 3. Elements of the product matrix are obtained by adding the products of appropriate row elements of the first matrix and elements of the appropriate column of the second matrix. Matrix multiplication is generally not commutative, as demonstrated in the next several cells. Products of vectors and matrices yield vectors as shown in the next cells. These products are also generally not commutative.
During the on‐resonance pulse, the rf magnetic field B1 is aligned in the xy plane at ϕ radians with respect to the x axis. During the pulse, the net magnetization precesses (“nutates”) around the B1 field. After rotating π/2 radians, the net magnetization M ends up in the xy plane at ϕ radians relative to the −y axis of the rotating frame, where it stays because the rf pulse is on resonance. 2. 4 Single pulse (π/2)x experiment, off‐resonance (δ ≠ 0). Before the pulse, the net magnetization M is aligned along the z axis.
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. All NMR experiments start with ˆ eq (ρdiff).