Introductory Quantum Mechanics - Network Pack: (A Computer Illustrated Text)

This text and the accompanying computer programmes have grown out of an introductory course in quantum mechanics to the author's second-year undergraduates at the University of York. It was intended from the outset that the book would include all the essentials of an introductory course in quantum mechanics and that it would be illustrated wherever appropriate with the aid of computer programmes. The computer aspect has influenced the content only in that one or two topics have been included which are more usually to be found in more advanced courses. Thus the partial-wave treatment of scattering is included. This lends itself to illustration by means of computer programmes and is readily accessible at the level of the rest of the book. The essential mathematical prerequisites are mechanics, differential and integral calculus, complex numbers, vectors and matrices. Much of the book is concerned with the solution of partial equations but the methods used are explained as required. Undoubtedly some familiarity with Fourier series and transforms will be of considerable aid in comprehension, but very little direct use is made of them. It is assumed that students will have already studied introductory modern physics, so only a brief chapter covering the absolute essential preliminaries is included. Then follows a chapter on the backbone of the entire book, Schrodinger's equation. Here and elsewhere the author tries to make clear what is postulated and what follows logically. Despite their mathematical complexity, the author felt the necessity to include here a brief description of wave-packets, because they provide a far better link with everyday experience than stationary states. Some material is included here, on probability flux, which some may prefer to skip on a first reading, and return to when the chapters on scattering are tackled.

Table of Contents:
Part 1: the need for the quantum mechanics; quantization of radiation; the special theory of relativity; wave-particle duality; the nature of matter waves; the uncertainty principle; the Bohr atom. Part 2 Schrodinger's equation: the postulates of quantum mechanics; the wave equation; the wave equation in three dimensions; the time-independent Schrodinger equation; stationary states; normalisation; probability flux; physical constraints on the wave-function; wave packets; Gaussian wave-packets and the uncertainty principle. Part 3 One-dimensional potential wells: potential wells; the one-dimensional infinite square well; discussion of infinite square-well results; eigenvalue equations; the finite square well; finite square well eigenfunctions; the control of the wave-function by the wave equation; numerical integration of Schrodinger's equation; continuum solutions of the square-well potential; interpretation of unbound-particle wave functions; the double potential well; the quantum bouncer; electric fields and the tilted well; the harmonic oscillator - introduction; the quantum oscillator; discussion of harmonic oscillator eigenvalues and eigenfunctions; the classical probability density; more potential wells. Part 4 Schrodinger's equation in three dimensions: particle in a three dimensional box; degeneracy; Schrodingers equation in spherical polar coordinates - the hydrogen atom; normalisation. Part 5 Formal development of quantum mechanics: eigenvalues equations, operators and measurements; the momentum operator, eigenvalues and eigenfunctions; the position operator and its eigenfunctions; Hermitian operators; orthogonality of eigenfunctions; the expansion postulate; example - the b-decay of tritium; expectation values; compatibility of observables - commutators; non-commuting operators; time-dependence of expectation values - Ehrenfest's theorem; abstract operators - the parity operator, matrix mechanics. Part 6 Angular momentum: angular momentum operators; angular momentum commutators; angular momentum eigenvalues and eigenfunctions; interpretation of angular momentum eigenvalues; interpretation of angular momentum eigenfunctions; the Stern-Gerlach apparatus and electron spin; spin operators - the Pauli Spin matrices; the Zeeman effect; measurements in quantum mechanics. Part 7 Spherically symmetric potential wells: the rigid rotator; the radial equation; the hydrogen atom and hydrogen like ions; the isotropic harmonic oscillator; molecular vibrations - the Morse potential; the spherical square well; general properties of spherically symmetric potential wells. (Part contents)