Quantum theory: an introduction to basics

George Frederick James Temple

Jarosław Adam Miszczak

We present a concise introduction of basic concepts in quantum information theory and quantum mechanics prepared as an introduction for a general audience. In our approach the rules of quantum mechanics are presented in a simple form of rules describing the method of constructing quantum objects corresponding to classical objects. As a byproduct of the introduced approach, we present some alternative rules and use them to describe basic ingredients of quantum information theory using different types of objects.

Hendrik F. Hameka

Mark S. Swanson

This extended and updated second edition course text presents a logical and concise introduction to the basic concepts, applications, and physical meaning of quantum mechanics. An initial review of classical mechanics and electromagnetism provides the reader with the context for quantum mechanics. Starting with atomic level experimental results, the probabilistic nature of quantum mechanics is derived, with the wave function related to the statistical theory of random variables. Applying the requirement of Galilean invariance yields the Schrödinger equation, and the Copenhagen interpretation of the wave function is discussed. After numerous basic applications of wave mechanics, including the hydrogen atom and the harmonic oscillator, the text then presents Dirac notation and Hilbert space theory. New chapters discuss perturbation theory, path integrals, scattering theory, and quantum entanglement. Key features • Extended and updated edition of a well-used textbook. • Offers a thorough connection to classical mechanics and electromagnetism. • Provides a logical development of basic quantum mechanical concepts and a connection to formal quantum mechanics. • Acts as a complete introduction to the most important quantum mechanical results in basic systems. • An introductory text that provides connections to the current research in quantum computing and measurement theory.

Michel Talagrand

This chapter provides a self-contained introduction to the basic aspects of Quantum Mechanics, focusing on what is must for Quantum Field Theory. The notions of state space, unitary operators, self-adjoint operators, and projective representation are covered as well as Heisenberg’s uncertainty principle. A complete proof of Stone’s theorem is given, but the spectral theory is covered only at the heuristic level. We provide an introduction to Dirac’s formalism, which is almost universally used in physics literature. The time-evolution is described in both the Schrödinger and the Heisenberg picture. A complete treatment of the harmonic oscillator, providing an introduction to the fundamental idea of creation and annihilation operators concludes the chapter.