Lecture 6 Quantum mechanical spin University （6自旋量子力学大学讲座）.pdfVIP

Lecture 6 Quantum mechanical spin Background Until now, we have focused on quantum mechanics of particles which are “featureless” – carrying no internal degrees of freedom. A relativistic formulation of quantum mechanics (due to Dirac and covered later in course) reveals that quantum particles can exhibit an intrinsic angular momentum component known as spin. However, the discovery of quantum mechanical spin predates its theoretical understanding, and appeared as a result of an ingeneous experiment due to Stern and Gerlach. Spin: outline 1 Stern-Gerlach and the discovery of spin 2 Spinors, spin operators, and Pauli matrices 3 Spin precession in a magnetic field 4 Paramagnetic resonance and NMR Background: expectations pre-Stern-Gerlach Previously, we have seen that an electron bound to a proton carries an orbital magnetic moment, e ˆ ˆ µ = L µB L/, Hint = µ · B 2me For the azimuthal component of the wavefunction, eim , to remain single-valued, we further require that the angular momentum takes only integer values (recall that m ). When a beam of atoms are passed through an inhomogeneous (but aligned) magnetic field, where they experience a force, ˆ F = (µ · B) µ ( B )e z z z z we expect a splitting into an odd integer (2 + 1) number of beams. Stern-Gerlach experiment In experiment, a beam of silver atoms were passed through inhomogeneous magnetic field and collected on photographic plate. Since silver involves spherically symmetric charge distribution plus one 5s electro