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Physics Bulletin

Classical Mechanics

I. I. Berenblut

Published Nov 1, 1959• 0 citations
Publisher

Abstract

By J. W. Leech London : Methuen & Co. Ltd. New York : John Wiley & Sons Inc. Pp. ix + 149. Price 12s. 6d. Classical Mechanics, that is the development of Newton's laws of motion into generalized forms suitable for all types of co-ordinate systems, formed the basis and inspiration for the newer concepts of Wave Mechanics. The book under review is a concise and well written introduction to both Quantum and Relativity Mechanics, via the traditional paths of Langrangian and Hamiltonian Functions and Variational Principles.

DOI
10.1088/0031-9112/10/11/016

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Assuming a background in basic classical physics, multivariable calculus, and differential equations, A Concise Introduction to Quantum Mechanics provides a self-contained presentation of the mathematics and physics of quantum mechanics. The relevant aspects of classical mechanics and electrodynamics are reviewed, and the basic concepts of wave-particle duality are developed as a logical outgrowth of experiments involving blackbody radiation, the photoelectric effect, and electron diffraction. The Copenhagen interpretation of the wave function and its relation to the particle probability density is presented in conjunction with Fourier analysis and its generalization to function spaces. These concepts are combined to analyze the system consisting of a particle confined to a box, developing the probabilistic interpretation of observations and their associated expectation values. The Schrödinger equation is then derived by using these results and demanding both Galilean invariance of the probability density and Newtonian energy-momentum relations. The general properties of the Schrödinger equation and its solutions are analyzed, and the theory of observables is developed along with the associated Heisenberg uncertainty principle. Basic applications of wave mechanics are made to free wave packet spreading, barrier penetration, the simple harmonic oscillator, the Hydrogen atom, and an electric charge in a uniform magnetic field. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented and used to analyze coherent states, the linear potential, two state oscillations, and electron diffraction. Applications are made to photon and electron spin and the addition of angular momentum, and direct product multiparticle states are used to formulate both the Pauli exclusion principle and quantum decoherence. The book concludes with an introduction to the rotation group and the general properties of angular momentum.
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.
David Park McGraw-Hill Publishing Co. Ltd. 1964. Pp. xv + 547. Price 83s. 6d. There are surely few branches of physics which have been so amply, and repetitively, documented as the basic principles of quantum mechanics. Suppressing an almost overwhelming impression of déjà vu, one opens this new entry to the field to find that the text is so organized as to present the discussion of the theory in Part I, and to segregate the applications to Part II, an arrangement for which there is much to be said and which, when as thoughtfully carried out as in the example under review, allows the student, and the lecturer, the opportunity to mix his own blend of theory and application.