Speaker
Description
Spin is typically the first encounter students have with intrinsically quantum degrees of freedom, yet its mathematical formalism is often postulated in an abstract manner that removes it from its experimental roots. We present a sophomore-level instructional approach in which the spin-1/2 formalism is developed directly from experimentally motivated phenomena. Beginning with Stern–Gerlach experiment, which motivates the z-component of spin operator as related to the experimental measurements, we also discuss magnetic resonance, which can transition the state from up to down (or vice versa), which motivates the spin raising and lowering operators. Commutation relations follow from these definitions because applying the product of two operators to a state depends on the order that they are applied. One also can quickly define the Cartesian spin operators and the total magnitude squared of spin by pushing the reasoning further. This allows you to fully develop the su(2) algebra from experimental considerations. With these results in hand, one can have students determine states of definite spin along arbitrary oriented axes. The approach emphasizes the connection between experimental procedures and mathematical structure, allowing students to see the algebra of spin as a logical consequence of empirical facts rather than as an abstract postulate. We describe how this approach fits into our teaching of quantum mechanics in a Modern Physics course. The work presented here is part of a project to re-envision the quantum mechanics component of a Modern Physics course to emphasize experiment and classical thinking as pillars upon which quantum mechanics is built.
