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

By Alan J. Benesi

Provides the idea of NMR more suitable with Mathematica© notebooks

  • Provides brief, centred 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 speculation within the type of textual content, images, sound, and calculations
  • Based on type proven tools constructed via the writer over his 25 yr instructing profession. those notebooks express precisely how the idea works and supply precious calculation templates for NMR researchers

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

Example text

4) Î2 I , m For example, the eigenvalue of Î2 for an I = 5/2 nuclear spin is 35/4. Many important operators for observable quantities are not eigenoperators. They do not yield real eigenvalues when acting on ψ. For example, the nuclear spin angular momentum operator Î is not an eigenoperator. Nor is the operator Î+, which is used to calculate or simulate the observable NMR signal, or the transverse ­operators Îx and Îy. 5) Op where the integration is over all space τ. 6) where is called the bra and is called the ket.

The answer is that the pure eigenstates are the only states that are stationary. That is, if a system is somehow prepared in a pure eigenstate it will stay there as long as the Hamiltonian does not change. This is indeed the case for electronic eigenstates for atoms and molecules where the eigenstates are separated by energies much greater than the average thermal energy but not for nuclear spin angular momentum where the eigenstates are separated by energies much less than the average thermal energy.

During the first τ delay, the magnetization M splits into two components, one precessing at 2π(+j/2) radian s−1 and one precessing at 2π(–j/2) around the +z axis. If τ is set to 1/(2 j), the two components of M are aligned with the +y and –y axes, respectively. Based on the vector model (Bloch equation), one expects the (π/2)y to bring about no change in the magnetization components. ” Why? Because the (π/2)y pulse has created unobservable zero and double quantum coherence. 1). 2). The major problem for the vector model occurs if acquisition starts after the second (π/2)y.

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