Notes 14 : Spins in Magnetic Fields

A nice illustration of rotation operator methods that is also important physically is the problem of spins in magnetic fields. The earliest experiments with spins in magnetic fields were those of Stern and Gerlach, which first revealed the quantization of electron spin. Similar but later experiments by Stern and other collaborators were used to make crude measurements of the proton magnetic moment and other nuclear magnetic moments. In the late 1930’s, these experiments were improved upon by Rabi, who developed the technique of spin flipping with time-dependent magnetic fields. With his new apparatus, Rabi was able to make much more accurate measurements of nuclear magnetic moments. After World War II, Bloch and Purcell developed methods for studying magnetic resonance in bulk samples (solid or liquid), by measuring microwave power absorbed at resonance or by looking at the time development and relaxation of induced magnetization. In the same period, Rabi’s beam techniques were improved upon by Ramsey. Modern applications of the magnetic resonance technique include measurements of nuclear magnetic moments and g-factors, measurements of diamagnetic shielding of external fields in molecules or solids (important in chemistry and solid state physics), the construction of sensitive magnetometers and atomic clocks, and tomography or imaging in medicine and biology.