Quantum Mechanics (eBook)

Professor Nouredine Zettili, Physical and Earth Sciences, Jacksonville State, University, Jacksonville, AL, USA 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.

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.

"The strength of the book lies in the long list of problems and the
detailed solutions that makes the book student-oriented,
especially, undergraduates. Teachers of the subject can benefit
from the end-of-chapter exercises for assignments." (Contemporary
Physics, 11 July 2011)

"The book contains almost six hundred examples, problems and
exercises, some of them fully solved. They are intended to empower
students to become independent learners and adept practitioners of
quantummechanics." (Mathematical Reviews, July 2010)

"Zettili provides a second edition of this textbook on
quantum mechanics. The material is suitable for two undergraduate
semesters and one graduate level semester." ( Book
News, September 2009)