Quantum Mechanics Concepts and Applications

Das reich illustrierte Lehrbuch führt in klarem, ausgewogenem und modernem Stil in die Quantenmechanik ein. Grundlegende Elemente der Theorie werden anschaulich mit Anwendungen verknüpft. Mehr als 65 durchgerechnete, Schritt für Schritt erklärte Aufgaben und über 150 mehrteilige Beispiele mit Lösungen erleichtern das Verständnis der mathematischen Hilfsmittel der Quantenmechanik. Ein Buch für Studenten und Dozenten!

Quantum Mechanics: Concepts and Applications provides a clear, balanced introduction aimed at students taking an introductory course in the subject. Written with the student's background and ability in mind, the book takes an innovative approach to quantum mechanics. The text successfully combines essential theory with many practical applications, illustrated by numerous examples and solved problems. Carefully structured, the text starts with the experimental basis of quantum mechanics before covering the mathematical tools, such as linear spaces, operator algebra, matrix mechanics and eigenvalue problems. Subsequent chapters cover the formal foundations of quantum mechanics, the exact solutions of the Schrodinger equation for one and three dimensional potentials, time independent and time–dependent approximation methods and then finally, the theory of scattering.

Assuming no prior knowledge of the subject, this richly illustrated text includes many worked examples and numerous problems with step–by step solutions designed to help the reader master the machinery of quantum mechanics.

Quantum Mechanics: Concepts and Applications;
* Provides a comprehensive introduction to quantum mechanics, combining both a theoretical and practical approach.

* Includes over 65 solved examples integrated throughout the text and each chapter concludes with an extensive collection of fully solved multipart problems.

* Offers an in–depth treatment of the practical mathematical tools of quantum mechanics.

* Devotes an entire section to the numerical solution of the one–dimensional Schrödinger equation, (including code)

This introductory text is aimed at all students taking a first course on quantum mechanics. It promises to become an invaluable tool not only for graduate students preparing for the preliminary and qualifying examinations but for teachers as well.

Preface.

Origins of Quantum Physics.

Historical Note.

Particle Aspect of Radiation.

Wave Aspect of Particles.

Particles versus Waves.

Indeterminacy of the Microphysical World.

Atomic Transitions and Spectroscopy.

Wave Packets.

Concluding Remarks.

Solved problems.

Exercises.

Mathematical Tools of Quantum Mechanics.

Introduction.

The Hilbert Space and Wave Functions.

Dirac Notations.

Operators.

Representation in Discrete Bases.

Representation in Continuous Bases.

Matrix and Wave Mechanics.

Concluding Remarks.

Solved Problems.

Exercises.

Postulates of Quantum Mechanics.

Introduction.

The Basic Postulates of Quantum Mechanics.

The State of a System.

Observables and Operators.

Measurement in Quantum Mechanics.

Time Evolution of the System's State.

Symmetries and Conservation Laws.

Connecting Quantum to Classical Mechanics.

Solved Problems.

Exercises.

One–Dimensional Problems.

Introduction.

Properties of One–Dimensional Motion.

The Free Particle: Continuous States.

The Potential Step.

The Potential Barrier and Well.

The Infinite Square Well Potential.

the Finite Square Well Potential.

The Harmonic Oscillator.

Numerical Solution of the Schrö dinger Equation.

Solved Problems.

Problems.

Angular Momentum.

Introduction.

Orbital Angular Momentum.

General Formalism of Angular Momentum.

Matrix Representation of Angular Momentum.

Geometrical Representation of Angular.

Momentum.

Spin Angular Momentum.

Eigenfunctions of Orbital Angular Momentum.

Solved Problems.

Exercises.

Three–Dimensional Problems.

Introduction.

3D Problems in Cartesian Coordinates.

3D Problems in Spherical Coordinates.

Concluding Remarks.

Solved Problems.

Exercises.

Rotations and Addition of Angular Momenta.

Rotations in Classical Physics.

Rotations in Quantum Mechanics.

Addition of Angular Momenta.

Scalar, Vector and Tensor Operators.

Solved Problems.

Exercises.

Identical Particles.

Many–Particle Systems.

Systems of Identical Particles.

The Pauli Exclusion Principle.

Solved Problems.

Problems.

Approximation Methods for Stationary States.

Introduction.

Time–Independent Perturbation Theory.

The Variational Method.

The Wentzel Kramers Brillouin Method.

Concluding Remarks.

Solved Problems.

Problems.

Time–Dependent Perturbation Theory.

Introduction.

The Pictures of Quantum Mechanics.

Time–Dependent Perturbation Theory.

Adiabatic and Sudden Approximations.

Interaction of Atoms with Radiation.

Solved Problems.

Exercises.

Scattering Theory.

Scattering and Cross Section.

The Scattering Amplitude of Spinless Particles.

The Born Approximation.

Partial Wave Analysis.

Scattering of Indentical Particles.

Solved Problems.

Exercises.

The Delta Function.

One–Dimensional Delta Function.

Three–Dimensional Delta Function.

Angular Momentum in Spherical Coordinates.

Computer Code for Solving the Schrö dinger.

Equation.

Index.

NOUREDINE ZETTILI received his Ph.D. in 1986 from MIT and is currently Professor of Physics at Jacksonville State University, USA. His research interests include nuclear theory, the many–body problem, quantum mechanics and mathematical physics. He has also published two booklets designed to help students improve their study skills.
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