Quantum Mechanics

Abstract

The preparation of another edition of a text on quantum mechanics is always a challenge. On the one hand, one may decide to cover some previously omitted topics, after gauging again their relevance. On the other hand, the fast evolution of the subject implies the need to incorporate not only new experimental facts and theoretical developments but also new concepts in the description of nature. Therefore, self-imposed constraints about the overall length of the book become strained. This is a good motivation for a revision. As a consequence, few items have been omitted and many more included, even some which are usually not discussed in introductory texts (like the breakdown of symmetries). The book consists of two main parts. The first one displays the following organization: As in the previous editions, the basic principles of quantum mechanics are introduced within the framework of Hilbert spaces. Their empirical consequences (both thought and real experiments) and theoretical implications (uncertainty relations, no-cloning theorem) are discussed. The Heisenberg matrix realization of the basic principles allows us to solve the two-state system, the harmonic oscillator and a combination of the two, the Jaynes–Cummings model. The Schr¨odinger realization covers conventional subjects, including both bound and scattering examples. The contrast between these two realizations underscores the appearance of the most important quantum observable, the spin. The description of many-body systems requires the distinction between fermions and bosons and the indistinguishability among each of the two types of particles. As a consequence of these two features, there appears another formulation of quantum mechanics, the so-called second quantization.