Math Fundamentals - NMR
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چکیده
Figure 1: Two electric fields are shown. Both have the same frequency, but differ in phase. The solid line has a phase shift of 0 , while the dotted line is shifted -120 . Complex numbers are widely used as a convenient method of keeping track of the frequency and phases of pulses and signals in NMR. In the case of x-ray crystallography, they provide a way of representing the effect of atomic position on the scattering of x-rays. A complex number is of the form z = a + ib, where a and b are real numbers. The symbol i is defined as i = √ −1. There are various ways to represent complex numbers. one of the most useful is a Argand diagram, shown in Fig. 2. In the Argand diagram the real (a) and imaginary (b) components of the complex number define the position of the point in a Cartesian system with the real and imaginary axis as the two basis, or coordinate axis. It is also possible to represent complex numbers in polar coordinates. The two representations are equivalent. The latter representation is more useful in NMR because the phase of the NMR signal can be obtained directly from the size of θ. The representation of the complex number in polar coordinates gives the following definition: z = r(cosθ + isinθ), (1)
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Fundamentals of Multiple-Quantum Magic-Angle Spinning NMR on Half-Integer Quadrupolar Nuclei
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تاریخ انتشار 2011