Quantum mechanics : theory and experiment / Mark Beck.

Includes bibliographical references and index.

Print version record.

Cover; Contents; Table of Symbols; Preface; 1 MATHEMATICAL PRELIMINARIES; 1.1 Probability and Statistics; 1.2 Linear Algebra; 1.3 References; 1.4 Problems; 2 CLASSICAL DESCRIPTION OF POLARIZATION; 2.1 Polarization; 2.2 Birefringence; 2.3 Modifying the Polarization; 2.4 Jones Vectors and Jones Matrices; 2.5 Polarization Interferometer; 2.6 References; 2.7 Problems; Complement to Chapter 2: 2.A: Coherence and Interference; 3 QUANTUM STATES; 3.1 State Vectors; 3.2 Basis States; 3.3 Other States; 3.4 Probabilities; 3.5 Complex Probability Amplitudes; 3.6 Row and Column Vector Notation.

3.7 Interference3.8 Problems; 4 OPERATORS; 4.1 Operators; 4.2 The Adjoint Operator; 4.3 The Projection Operator; 4.4 The Matrix Representation of Operators; 4.5 Changing Bases; 4.6 Hermitian Operators; 4.7 References; 4.8 Problems; Complement to Chapter 4: 4.A: Similarity Transformations; 5 MEASUREMENT; 5.1 Measuring Polarization; 5.2 The Postulates of Quantum Mechanics; 5.3 Expectation Values; 5.4 Operators and Measurements; 5.5 Commutation and Indeterminacy Relations; 5.6 Complementarity; 5.7 References; 5.8 Problems; Complement to Chapter 5: 5.A: ''Measuring'' a Quantum State; 6 SPIN-1/2.

6.1 The Stern-Gerlach Experiment6.2 Spin States; 6.3 More Spin States; 6.4 Commutation Relations; 6.5 Particle Interference; 6.6 References; 6.7 Problems; 7 ANGULAR MOMENTUM AND ROTATION; 7.1 Commuting Observables; 7.2 Angular Momentum Operators; 7.3 Eigenvalues and Eigenstates; 7.4 Spin-1; 7.5 Rotation; 7.6 Spin of a Photon; 7.7 References; 7.8 Problems; Complements to Chapter 7: 7.A: Compatible Observables; 7.B: Eigenvalues and Eigenstates of Angular Momentum; 8 TWO-PARTICLE SYSTEMS AND ENTANGLEMENT; 8.1 Pairs of Photons; 8.2 Entangled States; 8.3 Mixed States; 8.4 Testing Local Realism.

8.5 References8.6 Problems; Complements to Chapter 8: 8.A: The Density Operator; 8.B: The Bell-Clauser-Horne Inequality; 8.C: Two Spin-1/2 Particles; 9 TIME EVOLUTION AND THE SCHRÖDINGER EQUATION; 9.1 The Time-Evolution Operator; 9.2 The Schrödinger Equation; 9.3 Expectation Values; 9.4 Spin-1/2 Particle in a Magnetic Field; 9.5 Neutrino Oscillations; 9.6 References; 9.7 Problems; Complement to Chapter 9: 9.A: Magnetic Resonance; 10 POSITION AND MOMENTUM; 10.1 Position; 10.2 Momentum; 10.3 The Momentum Basis; 10.4 Problems; Complement to Chapter 10: 10.A: Useful Mathematics.

11 WAVE MECHANICS AND THE SCHRÖDINGER EQUATION11.1 The Schrödinger Equation Revisited; 11.2 Constant Potential-the Free Particle; 11.3 Potential Step; 11.4 Tunneling; 11.5 Infinite Square Well; 11.6 References; 11.7 Problems; Complement to Chapter 11: 11.A: Free Particle Propagation; 12 THE HARMONIC OSCILLATOR; 12.1 Why Study the Harmonic Oscillator?; 12.2 Creation, Annihilation, and Number Operators; 12.3 Wave Functions; 12.4 Fock States and Photons; 12.5 Coherent States; 12.6 References; 12.7 Problems; Complement to Chapter 12: 12.A: Solving the Schrödinger Equation Directly.

This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mathematics of a relatively simple system, before moving on to more complicated systems. After describing polarization, the text goes on to describe spin systems, time evolution, continuous variable systems (particle in a box, harmonic oscillator, hydrogen atom, etc.), and perturbation theory. The book also includes chapters which describe material that is frequently absent from undergraduate texts: quantum measurement, entanglement, quantum field theory and quantum information. This material is connected not only to the laboratories described in the text, but also to other recent experiments. Other subjects covered that do not often make their way into undergraduate texts are coherence, complementarity, mixed states, the density operator and coherent states. Supplementary material includes further details about implementing the laboratories, including parts lists and software for running the experiments. Computer simulations of some of the experiments are available as well. A solutions manual for end-of-chapter problems is available to instructors

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