Angular momentum spatial quantization

This situation is sketched in Fig. 3.5 where different polarizations are shown for J = 5/2. The system has axial symmetry around the preselected quantization axis (z-axis). The Mj-associated directions are indicated by the precessing angular momentum J, and the populations a(JMj) are characterized by the length of these precessing angular momenta. In this way one obtains a spatial view of (a) an aligned, (b) an isotropic, and (c) an oriented state. 

Fig. 3.7. Spatial quantization of the angular momentum Ja with quantum number J" = 3 at Q-absorbtion (x = 2) of linearly polarized light with E z. The figures show the values of M" = p. The solid line indicates the spatial distribution of Ja in the classic limit (J —> oo).

Let us first consider the normal Zeeman effect, which applies to transitions between electronic states with zero total spin magnetic moment, so-called singlet states. Like the projection Ms of S in the Stern-Gerlach experiment, the projection Ml of the spatial angular momentum L is space quantized in the external magnetic field. We shall describe the quantization of the spatial angular momentum by means of quantum mechanical methods in detail later. Suffice it to say that each state with spatial angular momentum quantum number L splits into 2L + 1 components, i.e., a P state (L = 1) splits into three components with... 

A further important aspect of optical pumping with a polarized laser is the selective population or depletion of degenerate M sublevels 17, M) of a level with angular momentum J. These sublevels differ by the projection Mtl of J onto the quantization axis. Atoms or molecules with a nonuniform population density N(J, M) of these sublevels are oriented because their angular momentum J has a preferred spatial distribution while under thermal equilibrium conditions J points into all directions with equal probability, that is, the orientational distribution is uniform. The highest degree of orientation is reached if only one of the (27+ 1) possible M sublevels is selectively populated. 

Because of the fact that not the absolute value of the angular momentums but their projections are measurable quantities, it can often be said that the electron spin is (1/2)S or simply (1/2). The spin spatial quantization is depicted in Figure 7.21. 

In conclusion, we have established that the precession gives a gain of additional energy. Therefore, to treat spatial quantization of the angular momentum (7.5.3) as precession is incorrect from our point of view, because this effect does not produce any specific energy. 

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