Quantum Mechanics. Concepts and Applications. 2nd Edition

  • ID: 2335434
  • Book
  • 688 Pages
  • John Wiley and Sons Ltd
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Quantum Mechanics: Concepts and Applications provides a clear, balanced and modern introduction to the subject. Written with the student s background and ability in mind the book takes an innovative approach to quantum mechanics by combining the essential elements of the theory with the practical applications: it is therefore both a textbook and a problem solving book in one self–contained volume. Carefully structured, the book starts with the experimental basis of quantum mechanics and then discusses its mathematical tools. Subsequent chapters cover the formal foundations of the subject, the exact solutions of the Schrödinger equation for one and three dimensional potentials, time–independent and time–dependent approximation methods, and finally, the theory of scattering.

The text is richly illustrated throughout with many worked examples and numerous problems with step–by–step solutions designed to help the reader master the machinery of quantum mechanics. The new edition has been completely updated and a solutions manual is available on request.

Suitable for senior undergradutate courses and graduate courses.

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Preface.

1. Origins of Quantum Physics.

1.1 Historical Note.

1.2 Particle Aspect of Radiation.

1.3 Wave Aspect of Particles.

1.4 Particles versus Waves.

1.5 Indeterministic Nature of the Microphysical World.

1.6 Atomic Transitions and Spectroscopy.

1.7 Quantization Rules.

1.8 Wave Packets.

1.9 Concluding Remarks.

1.10 Solved Problems.

Exercises.

2. Mathematical Tools of Quantum Mechanics.

2.1 Introduction.

2.2 The Hilbert Space and Wave Functions.

2.3 Dirac Notation.

2.4 Operators.

2.5 Representation in Discrete Bases.

2.6 Representation in Continuous Bases.

2.7 Matrix and Wave Mechanics.

2.8 Concluding Remarks.

2.9 Solved Problems.

Exercises.

3. Postulates of Quantum Mechanics.

3.1 Introduction.

3.2 The Basic Postulates of Quantum Mechanics.

3.3 The State of a System.

3.4 Observables and Operators.

3.5 Measurement in Quantum Mechanics.

3.6 Time Evolution of the System s State.

3.7 Symmetries and Conservation Laws.

3.8 Connecting Quantum to Classical Mechanics.

3.9 Solved Problems.

Exercises.

4. One–Dimensional Problems.

4.1 Introduction.

4.2 Properties of One–Dimensional Motion.

4.3 The Free Particle: Continuous States.

4.4 The Potential Step.

4.5 The Potential Barrier and Well.

4.6 The Infinite Square Well Potential.

4.7 The Finite Square Well Potential.

4.8 The Harmonic Oscillator.

4.9 Numerical Solution of the Schrödinger Equation.

4.10 Solved Problems.

Exercises.

5. Angular Momentum.

5.1 Introduction.

5.2 Orbital Angular Momentum.

5.3 General Formalism of Angular Momentum.

5.4 Matrix Representation of Angular Momentum.

5.5 Geometrical Representation of Angular Momentum.

5.6 Spin Angular Momentum.

5.7 Eigen functions of Orbital Angular Momentum.

5.8 Solved Problems.

Exercises.

6. Three–Dimensional Problems.

6.1 Introduction.

6.2 3D Problems in Cartesian Coordinates.

6.3 3D Problems in Spherical Coordinates.

6.4 Concluding Remarks.

6.5 Solved Problems.

Exercises.

7. Rotations and Addition of Angular Momenta.

7.1 Rotations in Classical Physics.

7.2 Rotations in Quantum Mechanics.

7.3 Addition of Angular Momenta.

7.4 Scalar, Vector and Tensor Operators.

7.5 Solved Problems.

Exercises.

8. Identical Particles.

8.1 Many–Particle Systems.

8.2 Systems of Identical Particles.

8.3 The Pauli Exclusion Principle.

8.4 The Exclusion Principle and the Periodic Table.

8.5 Solved Problems.

Exercises.

9. Approximation Methods for Stationary States.

9.1 Introduction.

9.2 Time–Independent Perturbation Theory.

9.3 The Variational Method.

9.4 The Wentzel "Kramers" Brillou in Method.

9.5 Concluding Remarks.

9.6 Solved Problems.

Exercises.

10. Time–Dependent Perturbation Theory.

10.1 Introduction.

10.2 The Pictures of Quantum Mechanics.

10.3 Time–Dependent Perturbation Theory.

10.4 Adiabatic and Sudden Approximations.

10.5 Interaction of Atoms with Radiation.

10.6 Solved Problems.

Exercises.

11. Scattering Theory.

11.1 Scattering and Cross Section.

11.2 Scattering Amplitude of Spinless Particles.

11.3 The Born Approximation.

11.4 Partial Wave Analysis.

11.5 Scattering of Identical Particles.

11.6 Solved Problems.

Exercises.

A. The Delta Function.

A.1 One–Dimensional Delta Function.

A.2 Three–Dimensional Delta Function.

B. Angular Momentum in Spherical Coordinates.

B.1 Derivation of Some General.

B.2 Gradient and Laplacianin Spherical Coordinates.

B.3 Angular Momentum in Spherical Coordinates.

C. Computer Code for Solving the Schrödinger Equation.

Index.

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Nouredine Zettili
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