CLASSICAL AND QUANTUM SPIN Nle 31'\"er The quantum mechanical Stern-Gerlach experiment In Worksheet 1, you examined the classical consequences of the Stem-Gerlach experiment. You will now consider the same situation with quantum mechanical particles. A Stern-Gerlach experimentusing the same magnetic eld as in Section II of Worksheet 1 is conducted on a beam of electrons. (The diagram of the setup is reproduced at right.) The picture below and to the right shows the distribution of electrons on the screen after a large number of electrons have passed through the magnetic eld. (The screen is represented by the vertical black line, and the red line indicates the center of the screen.) Top of Screen A. Are these results the same as what you would obtain with classical particles, as seen in the tutorial Panopto video? If not, explain how these results are different. Bottom of Screen This experiment suggests that the electron has a magnetic moment if. Suppose the same magnetic force law that applies to classical particles (in a magnetic eld = 322 with B, independent of x and y), 33 mag = #zazzzl also applies to the electron. B. Based on this magnetic force law and on the experimental distribution of electrons shown above, what can you conclude about the z-component of the magnetic moment, #2, of an electron? Explain. (Note: Assume here that B2 is a linear function of z.) C. Suppose the rst electron is observed to strike the upper spot on the screen in the above diagram (above the red line). Is the z-component of the magnetic moment, #2, for this electron positive, negative, or zero? Explain. D. Which of the two spots on the screen would you expect an electron to strike if its p, value was positive? Explain. The electron has a magnetic moment due to a property known as spin. This property is analogous to the classical angular momentum of a charged sphere spinning about an axis through its center, although there is no experimental evidence that something is spinning inside an electron. Quantum mechanical Spin is different from classical spinning in additional ways that will be explored in this course