1.1.The Stern-Gerlach Experiment Z-axis Beam direction Over To detector B-field Shaped limating Sli magnet (pole pieces) FIGURE 1.1.The Stern-Gerlach experiment proportional to the electron spin S, μaS (1.1.1) where the precise proportionality factor turns out to be e/m c(e <0 in this book)to an accuracy of about 0.2%. the interaction energy of the magnetic moment with the magnetic field is just-u.B,the z-component of the force experienced by the atom is given by aB. F=2(uB):a2 (1.1.2) where we have ignored the components of B in directions other than the z-direction.Because the atom as a whole is very heavy,we expect that the classical concept of trajectory can be legitimately applied,a point which can be justified using the Heisenberg uncertainty p derived late With the arrangement of Figure 1.1,the(S)atom experiencesa downward force,while the u.<0(S.>0)atom experiences an upward force.The beam is then expected to get split according to the values of u. In other words,the SG(Stern-Gerlach)apparatus"measures"the z-comp nent of or,equivalently,the z-component of S up to a proportionality factor. The atoms in the oven are randomly oriented;there is no preferred direction for the orientation of u.If the electron were like a classical spinning object we wo expect all values oftobe realized between and-lul.This would lead us to expect a continuous bundle of beams coming out of the SG apparatus,as shown in Figure 1.2a.Instead,what we