# Download e-book for iPad: Analytic geometry by Edwin S. Crawley, Henry B. Evans By Edwin S. Crawley, Henry B. Evans

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Extra resources for Analytic geometry

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G. the draw direction of fibres) is aligned along the Do field. g. 8 Powder spectra for various asymmetry parameters 11. The isotropic shift is set to w = O. With the convention used in the text, the W z edge of the spectrum is always located at w = o. e. Wx = -! O and 0 [i, e. (11). The spectra are normalized to equal integral (area). Near the Wz edge of the spectrum, the spectral lineshape hardly changes with 11. 3 the spectral features of the 11 = 0 spectrum can often be regarded as a good approximation.

8 Powder spectra for various asymmetry parameters 11. The isotropic shift is set to w = O. With the convention used in the text, the W z edge of the spectrum is always located at w = o. e. Wx = -! O and 0 [i, e. (11). The spectra are normalized to equal integral (area). Near the Wz edge of the spectrum, the spectral lineshape hardly changes with 11. 3 the spectral features of the 11 = 0 spectrum can often be regarded as a good approximation. 5: the spectral intensity over the interval [w ... w + dw] is proportional to the unit-sphere surface area between equifrequency lines at wand w + dw.

5 Quantum-mechanical calculations of NMR time evolutions So far we have discussed general Hamiltonians and the spectra that result for singlespin or two-spin interactions. The relationship between Hamiltonians and frequencies was introduced only on the basis of the semiclassical precession picture. In this section, we shall describe its quantum-mechanical foundation. The density-operator description of spin systems, which combines quantum mechanics and statistical mechanics, will be discussed, and it will be shown how the quantum-mechanical time evolutions can be calculated in practice.