Precession of Nuclear Magnetic Moments

Often it is convenient to have a pictorial representation of the behavior of nuclear magnetic moments. It is possible to use purely classical mechanics to develop a vector picture of the motion of a nuclear moment that is useful and to some extent correct. However, the classical approach to a system that is clearly quantum mechanical in nature is unsatisfying and can lead to misunderstandings. Fortunately, an equally appealing picture can be obtained directly from simple wave mechanical considerations. 

We consider, for simplicity, a spin /2 nucleus, with eigenfunctions a and /3, as described in Section 2.3. Note that a and /3 represent stationary eigenstates, but this does not imply that a nuclear spin must reside only in one of them. A general, time-dependent wave function can be constructed as a linear combination (or 

To obtain a picture of the way in which the magnetic moment behaves, let us consider the expectation values of the three components of fx, or alternatively, in accord with Eq. 2.1, the expectation values of the x, y, and z components, of I  

33 the time dependence in the exponentials cancels out when the complex conjugates are multiplied, and the two cross terms give zero because of 

The expectation values of Ix and Iy are obtained in a similar manner but give very different results  

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