Quantum Mechanics in a Nutshell

Quantum Mechanics in a Nutshell

Quantum mechanics is a mathematical description of the motion and interaction of elementary particles. Covering the basics of the field as well as many topics of current interest, Quantum Mechanics in a Nutshell offers a concise and accessible introduction to this powerful branch of physics. One-, two- and three-dimensional problems Looking for a top-notch guide through a subject notorious for its anti-intuitive concepts? Gerald Mahan is your man! Emphasizing the use of quantum mechanics to describe atoms and solids, Mahan’s book describes the properties of a single particle in potential; solves for two particles (e.g., the helium atom); addresses many-particle systems; and more. Applications include electron gas, magnetism and Bose-Einstein condensation. As Mahan explains in his introductory chapter, quantum mechanics is based on the wave-particle dual description formulated by Bohr, Einstein, Heisenberg, Schrödinger and others. The basic units of nature are indeed particles, but the description of their motion involves wave mechanics. The so-called wave function is the fundamental function for a single particle; the particle’s position at a given time is described as a probability by the square of the function. Following the introduction, we turn to the study of one-dimensional problems and their exact solutions. Here Mahan addresses the square well and linear potentials, as well as the harmonic oscillator, exponential potential and more. Instead of immediately proceeding with more advanced problems in dimensions higher than one, the book offers a chapter that shows how to solve Schrödinger’s equation using a pair of approximate methods: WKBJ and variational. We see how each of these methods can be used to describe the harmonic oscillator and other systems. Following this is a chapter devoted to spin and angular momentum. Angular momentum is an important entity in quantum mechanics; the two main contributors to the angular momentum are the spin of the particle and the orbital angular momentum from the rotational motion. Mahan derives the eigenfunctions and eigenvalues for both spin and orbital angular momentum. We next come to problems involving two and three dimensions. Nuclei, atoms, solids and stars are all examples of systems that must be solved in three dimensions. In contrast, two-dimensional solutions are required when a particle is restricted to move on a surface; examples include electrons moving on the surface of liquid helium or in a semiconductor quantum well. We find that many of techniques developed in prior chapters can be applied to two and three dimensions. From matrix methods to scattering theory The second half of the book features chapters on matrix methods and perturbation theory, time-dependent perturbations and electromagnetic radiation. There are also introductions to many-particle systems, scattering theory and relativistic quantum mechanics. Mahan explains how electromagnetic radiation is composed of elementary particles called photons. Massless and chargeless, they possess a specific momentum, energy and frequency. The correspondence between the classical electric field and the quantum picture of photons is that the intensity of light is proportional to the number of photons. The main difference between the classical and quantum picture is that in classical physics, the electric field can have any value whereas in quantum physics the number of quanta in a given volume must be an integer. Up until the final chapter, the book is concerned with nonrelativistic quantum mechanics, where the basic equation is Schrödinger’s equation. However, this equation does not apply when particles have kinetic energies of the same size as their rest energy. In these situations, we require a full relativistic equation. Accordingly, Mahan discusses two different equations of this type: Klein-Gordon and Dirac. The first of these applies to spinless particles

Hardcover: 414 pages

Publisher: Princeton University Press ( March 01, 2009 )

Item #: 02-6986

ISBN: 9780691137131

Product Dimensions: 7.0 x 10.0 x 0.0 inches

Product Weight: 29.0 ounces