The Bloch equations. How to have fun calculating what happens in NMR experiments with a personal computer

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Abstract
The so‐called “phenomenological” differential equations derived for nuclear magnetic induction by Felix Bloch in 1946 can easily be integrated by numerical methods and can give interesting, as well as very useful, results with the processing power of ordinary personal computers. This article deals with (1) the derivation of the Bloch equations, (2) slow‐passage continuous‐wave (CW) spectral calculations, (3) a procedure for numerical integration and several illustrations of how numerical integration can be used for generation of CW spectra, (4) free induction decays, and (5) the results of multipulse sequences, such as those used in determination of T1 and T2. A listing of the source code of a simple BASIC program for numerical integration of the Bloch equations with personal computers is included in an appendix.

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