Problems in quantum mechanics : with solutions

Problem solving in physics is not simply a test of understanding of the subject, it is an integral part of learning it. In this book, the key ideas of quantum mechanics are well illustrated by a carefully chosen set of problems complete with detailed, step-by-step solutions. Beginning with a chapter on orders of magnitude, a variety of topics is then covered, including the mathematical foundations of quantum mechanics, Schrödinger's equation, angular momentum, the hydrogen atom, the harmonic oscillator, spin, time-independent and time-dependent perturbation theory, the variational method, multielectron atoms, transitions and scattering. Throughout, the physical interpretation or application of certain results is highlighted, thereby providing useful insights into a wide range of systems and phenomena. There is considerable emphasis on applications to atomic, nuclear, and solid-state physics and this book will be invaluable to a wide range of physics undergraduates. Problem solving in physics is not simply a test of understanding the subject, but is an integral part of learning it. In this book, the basic ideas and methods of quantum mechanics are illustrated by means of a carefully chosen set of problems, complete with detailed, step-by-step solutions.After a preliminary chapter on orders of magnitude, a variety of topics is covered, including the postulates of quantum mechanics, Schrödinger's equation, angular momentum, the hydrogen atom, the harmonic oscillator, spin, time-independent and time-dependent perturbation theory, the variational method, identical particles, multielectron atoms, transitions and scattering. Most of the chapters start with a summary of the relevant t6heory, outlining the required background for a given group of problems.Considerable emphasis is placed on examples from atomic, solid-state and nuclear physics, particularly in the latter part of the book as the student's familiarity with the concepts and techniques increases.Throughout, the physical interpretation or application of the results is highlighted, thereby providing useful insights into the wide range of systems and phenomena. This approach will make the book invaluable to anyone taking an undergraduate course in quantum mechanics These papers were presented at the first EC-TMR Nonlinear Control Network Workshop, on Stability and Stabilization of Nonlinear Systems, that took place in March 1999, Ghent, Belgium. The TMR programme offers a unique opportunity for the academic community to expand their knowledge, share their experience and identify and discuss strategic issues in aspects of nonlinear control engineering. The aim is to create a resource centre of available expertise and research interests. This outstanding reference volume presents current and emerging research directions, including: Stability analysis of nonlinear dynamical systems and converse Lyapunov theorems; Stabilization and regulation of nonlinear dynamical control systems; Control of physical systems using physics-based Lyapunov functions and passivity, as well as bifurcation analysis and optimal control. This collection of peer-reviewed papers provides a comprehensive overview of this field of research for graduate students and researchers in engineering and applied mathematics. Problem solving in physics is not simply a test of understanding the subject, but is an integral part of learning it. In this book, the basic ideas and methods of quantum mechanics are illustrated by means of a carefully chosen set of problems, complete with detailed, step-by-step solutions. After a preliminary chapter on orders of magnitude, a variety of topics is covered, including the postulates of quantum mechanics. Schrodinger's equation, angular momentum, the hydrogen atom, the harmonic oscillator, spin, time-independent and time-dependent perturbation theory, the variational method, identical particles, multielectron atoms, transitions and scattering. Most of the chapters start with a summary of the relevant theory outlining the required background for a given group of problems. Considerable emphasis is placed on examples from atomic, solid-state and nuclear physics, particularly in the latter part of the book as the student's familiarity with the concepts and techniques increases.

Problem solving in physics is not simply a test of understanding of the subject, it is an integral part of learning it. In this book, the key ideas of quantum mechanics are well illustrated by a carefully chosen set of problems complete with detailed, step-by-step solutions. Beginning with a chapter on orders of magnitude, a variety of topics is then covered, including the mathematical foundations of quantum mechanics, Schrödinger's equation, angular momentum, the hydrogen atom, the harmonic oscillator, spin, time-independent and time-dependent perturbation theory, the variational method, multielectron atoms, transitions and scattering. Throughout, the physical interpretation or application of certain results is highlighted, thereby providing useful insights into a wide range of systems and phenomena. There is considerable emphasis on applications to atomic, nuclear, and solid-state physics and this book will be invaluable to a wide range of physics undergraduates.

Many students find quantum mechanics conceptually difficult when they first encounter the subject. In this book, the postulates and key applications of quantum mechanics are well illustrated by means of a carefully chosen set of problems, complete with detailed, step-by-step solutions. Beginning with a chapter on orders of magnitude, a variety of topics are then covered, including the mathematical foundations of quantum mechanics, Schrödinger's equation, angular momentum, the hydrogen atom, the harmonic oscillator, spin, time-independent and time-dependent perturbation theory, the variational method, multielectron atoms, transitions and scattering. Throughout, the physical interpretation or application of certain results is highlighted, thereby providing useful insights into a wide range of systems and phenomena. This approach will make the book invaluable to anyone taking an undergraduate course in quantum mechanics. This volume presents research directions, including: stability analysis of nonlinear dynamical systems and converse Lyapunov theorems; stabilization and regulation of nonlinear dynamical control systems; and control of physical systems using physics-based Lyapunov functions and passivity. G.l. Squires. Includes Bibliographical References (p. 250) And Index.