Chapter 31. Intrinsic Spin

Dennis Morris

Bahram Mashhoon, Helmut Kaiser

Alastair I. M. Rae, Jim Napolitano

The early twentieth century saw two major revolutions in the way physicists understand the world. One was quantum mechanics itself and the other was the theory of relativity. Important results also emerged when these two ideas were brought together: some of these have been referred to in earlier chapters-in particular the fact that fundamental particles such as electrons have intrinsic angular momentum (spin) was stated to be a relativistic effect. This chapter explores the relationship between relativity and quantum mechanics more deeply A full understanding of relativistic quantum mechanics is well outside the scope of this book, but many of the important results can be understood at this level and these will be discussed in this chapter. After a short summary of the main results of special relativity, we show how combining this with the time-dependent Schro¨dinger equation leads to a new wave equation known as the Dirac equation. We show how the Dirac equation requires particles such as electrons to have intrinsic angular momentum (spin) and we explore some of its other consequences. The chapter concludes with an outline of some more advanced ideas known as quantum field theory.

Ronald A. Lovett

Yu. M. Bunkov, Григорий Ефимович Воловик

This chapter discusses different phases of magnon superfluidity, including those in a magnetic trap; and signatures of magnon superfluidity: (i) spin supercurrent, which transports the magnetization for a macroscopic distance (up to 1 cm); (ii) spin current Josephson effect, which shows the interference between two condensates; (iii) spin current vortex — a topological defect which is an analog of a quantized vortex in superfluids, of an Abrikosov vortex in superconductors, and cosmic strings in relativistic theories; and (iv) Goldstone modes related to broken U(1) symmetry — phonons in the spin-superfluid magnon gas. The chapter also considers the topic of spin supercurrent in general, including spin-Hall and intrinsic quantum spin-Hall effects.

F. S. Levin

Thus far we have concentrated on the postulates, on their ramifications, and on the means and methods by which they are applied. Connections with classical physics have been featured, and primary notions other than those of Chapter 5 have not been needed. We deviate from this path in the present chapter, introducing a new and extremely important concept; it is based on one of the most significant and fruitful experiments of the quantal era. This experiment was performed by O. Stern and W. Gerlach (1921) and subsequently interpreted by G. Uhlenbeck and S. Goudsmit (1925). The experiment and its elucidation led to the new concept of “intrinsic spin” (in particular to spin “½”), a development that was one of the major turning points in modern physics. The consequences have been monumental, and include primary theoretical developments; the interpretation of data related to, and an understanding of, empirical rules concerning a wide variety of physical systems (e.g., the periodic table of the elements/atomic structure); and the generation of new experimental techniques and of innovative measurements. Our study of intrinsic spin and its correlative, two-state systems, introduces the reader to one of the most profound topics in quantum theory. The Stern–Gerlach experiment and its interpretation The experiment of Stern and Gerlach was designed to test the “spatial quantization” of neutral atoms, i.e., to determine whether the (orbital) angular momentum was quantized. The basic ideas are as follows. Associated with the atom's orbital angular momentum would be a magnetic moment, as in the Bohr model of hydrogen.