  The Stern-Gerlach experiment has played a central role in the discovery of
spin angular momentum. It can also play a pivotal role in teaching the
formalism of quantum mechanics using a concrete example involving a
finite-dimensional Hilbert space. Using this context, students can learn about
how to prepare a specific quantum state starting from an arbitrary state,
issues related to the time evolution of the wave function, and quantum
measurement. It can also be exploited to teach students about the distinction
between the physical space where one performs the experiment and the Hilbert
space where the state of the system lies and how the information about the
state of the system in the Hilbert space can be exploited to interpret the
possible outcomes of the experiment in the physical space. Students can learn
the advantages of choosing an appropriate basis to make suitable predictions
about the outcomes of experiments with different arrangements of Stern-Gerlach
devices. This experiment can also help students understand that an ensemble of
identically prepared systems, e.g., one in a linear superposition of two
stationary states, is not the same as a mixture, e.g., in which half of the
systems are in one stationary state and the other half are in the other
stationary state. Here, we discuss investigation of students' difficulties
about the Stern-Gerlach experiment by giving written tests and interviewing
advanced undergraduate and graduate students in quantum mechanics courses. We
also discuss preliminary data from two quantum mechanics courses that suggest
that a Quantum Interactive Learning Tutorial (QuILT) related to the
Stern-Gerlach experiment is helpful in improving students' understanding of
these concepts.
