Advanced quantum theory : an outline of the fundamental ideas

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.

Kenneth Watson

Alice Sinatra

Spin-squeezing is a well-established “quantum technology,” where well-designed correlations in an ensemble of two-level systems reduce the statistical uncertainty of spectroscopic experiments. This paper reviews some important advances in the field, with emphasis on the author's contributions concerning, in particular, the fundamental limits imposed by decoherence. Building on the material presented in the first part, new ideas and some promising developments are outlined in the last section.

P. Román, Peter B. Kahn

MICHAEL D. SCADRON

Yehuda Shadmi

An approach to the teaching of the chapter ’’Equivalent particles and the exclusion principle’’ (which is part of an undergraduate quantum mechanics course) is outlined. The clarification of basic concepts and the preventive treatment of anticipated beginners’ misunderstandings are emphasized. The exclusion principle is taught by confronting it with the principle of the ’’identity of the indiscernible’’ of Leibnitz. The limits of the analogy between general ideas belonging to different disciplines are outlined by discussing the inability of philosophy to predict the directions in which the physical theory actually advances.