< Previous  Index  Next >Chapter Summary:3. Particles with SpinThis chapter introduces the spin as an important intrinsic property of electrons. We discuss, in particular, some results that are relevant for atomic physics. More results will be presented from a slightly more abstract point of view in Chapter 4. In Section 3.5, we describe the mathematical consequences of this assumption. We construct a Hilbert space for particles with spin 1/2 and define the operators describing the components of the spin. In Section 3.6, we define the Pauli operator, that is, the Hamiltonian for a spin1/2 particle in an external field. We discuss the solutions in a constant, homogeneous magnetic field, thereby generalizing results from Book One in Section 3.7. An important difference from the results without spin is the occurence of bound states with zero energy. This phenomenon also occurs for nonhomogeneous magnetic fields and for certain situations in three dimensions (Section 3.8). The spin is most important for understanding finer details of the spectrum of hydrogenic atoms. In Section 3.9, we introduce the spinorbit coupling and describe the spinor eigenfunctions of the hydrogen atom and the structure of the energy spectrum. 



