Free download Quantum Mechanics Concepts and Applications By Nouredine Zettili Second Edition

Second Edition

Authors of:  Quantum Mechanics Concepts and Applications By Nouredine Zettili Second Edition

Nouredine Zettili

Table of Contents in Quantum Mechanics Concepts and Applications By Nouredine Zettili Second Edition

Preface to the Second Edition  

Preface to the First Edition  

Note to the Student  

1 Origins of Quantum Physics  

1.1 Historical Note  

1.2 Particle Aspect of Radiation  

1.2.1 Blackbody Radiation  

1.2.2 Photoelectric Effect  

1.2.3 Compton Effect  

1.2.4 Pair Production  

1.3 Wave Aspect of Particles  

1.3.1 de Broglie’s Hypothesis: Matter Waves  

1.3.2 Experimental Confirmation of de Broglie’s Hypothesis  

1.3.3 Matter Waves for Macroscopic Objects  

1.4 Particles versus Waves  

1.4.1 Classical View of Particles and Waves  

1.4.2 Quantum View of Particles and Waves  

1.4.3 Wave–Particle Duality: Complementarity  

1.4.4 Principle of Linear Superposition  

1.5 Indeterministic Nature of the Microphysical World  

1.5.1 Heisenberg’s Uncertainty Principle  

1.5.2 Probabilistic Interpretation  

1.6 Atomic Transitions and Spectroscopy  

1.6.1 Rutherford Planetary Model of the Atom  

1.6.2 Bohr Model of the Hydrogen Atom  

1.7 Quantization Rules  

1.8 Wave Packets  

1.8.1 Localized Wave Packets  

1.8.2 Wave Packets and the Uncertainty Relations  

1.8.3 Motion of Wave Packets  

1.9 Concluding Remarks  

1.10 Solved Problems  

1.11 Exercises  

2 Mathematical Tools of Quantum Mechanics  

2.1 Introduction  

2.2 The Hilbert Space and Wave Functions  

2.2.1 The Linear Vector Space  

2.2.2 The Hilbert Space  

2.2.3 Dimension and Basis of a Vector Space  

2.2.4 Square-Integrable Functions: Wave Functions  

2.3 Dirac Notation  

2.4 Operators  

2.4.1 General Definitions  

2.4.2 Hermitian Adjoint  

2.4.3 Projection Operators  

2.4.4 Commutator Algebra  

2.4.5 Uncertainty Relation between Two Operators  

2.4.6 Functions of Operators  

2.4.7 Inverse and Unitary Operators  

2.4.8 Eigenvalues and Eigen vectors of an Operator  

2.4.9 Infinitesimal and Finite Unitary Transformations  

2.5 Representation in Discrete Bases  

2.5.1 Matrix Representation of Kets, Bras, and Operators  

2.5.2 Change of Bases and Unitary Transformations  

2.5.3 Matrix Representation of the Eigenvalue Problem  

2.6 Representation in Continuous Bases  

2.6.1 General Treatment  

2.6.2 Position Representation  

2.6.3 Momentum Representation  

2.6.4 Connecting the Position and Momentum Representations  

2.6.5 Parity Operator  

2.7 Matrix and Wave Mechanics  

2.7.1 Matrix Mechanics  

2.7.2 Wave Mechanics  

2.8 Concluding Remarks  

2.9 Solved Problems  

2.10 Exercises  

3 Postulates of Quantum Mechanics  

3.1 Introduction  

3.2 The Basic Postulates of Quantum Mechanics  

3.3 The State of a System  

3.3.1 Probability Density  

3.3.2 The Superposition Principle  

3.4 Observables and Operators  

3.5 Measurement in Quantum Mechanics  

3.5.1 How Measurements Disturb Systems  

3.5.2 Expectation Values  

3.5.3 Complete Sets of Commuting Operators (CSCO)  

3.5.4 Measurement and the Uncertainty Relations  

3.6 Time Evolution of the System’s State  

3.6.1 Time Evolution Operator  

3.6.2 Stationary States: Time-Independent Potentials  

3.6.3 Schrödinger Equation and Wave Packets  

3.6.4 The Conservation of Probability  

3.6.5 Time Evolution of Expectation Values  

3.7 Symmetries and Conservation Laws  

3.7.1 Infinitesimal Unitary Transformations  

3.7.2 Finite Unitary Transformations  

3.7.3 Symmetries and Conservation Laws  

3.8 Connecting Quantum to Classical Mechanics  

3.8.1 Poisson Brackets and Commutators  

3.8.2 The Ehrenfest Theorem  

3.8.3 Quantum Mechanics and Classical Mechanics  

3.9 Solved Problems  

3.10 Exercises  

4 One-Dimensional Problems  

4.1 Introduction  

4.2 Properties of One-Dimensional Motion  

4.2.1 Discrete Spectrum (Bound States)  

4.2.2 Continuous Spectrum (Unbound States)  

4.2.3 Mixed Spectrum  

4.2.4 Symmetric Potentials and Parity  

4.3 The Free Particle: Continuous States  

4.4 The Potential Step  

4.5 The Potential Barrier and Well  

4.5.1 The Case E V0  

4.5.2 The Case E < V0: Tunneling  

4.5.3 The Tunneling Effect  

4.6 The Infinite Square Well Potential  

4.6.1 The Asymmetric Square Well  

4.6.2 The Symmetric Potential Well  

4.7 The Finite Square Well Potential  

4.7.1 The Scattering Solutions (E > V0)  

4.7.2 The Bound State Solutions (0 < E < V0)  

4.8 The Harmonic Oscillator  

4.8.1 Energy Eigenvalues  

4.8.2 Energy Eigen states  

4.8.3 Energy Eigen states in Position Space  

4.8.4 The Matrix Representation of Various Operators  

4.8.5 Expectation Values of Various Operators  

4.9 Numerical Solution of the Schrödinger Equation  

4.9.1 Numerical Procedure  

4.9.2 Algorithm  

4.10 Solved Problems  

4.11 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  

5.6.1 Experimental Evidence of the Spin  

5.6.2 General Theory of Spin  

5.6.3 Spin 1/2 and the Pauli Matrices  

5.7 Eigen functions of Orbital Angular Momentum  

5.7.1 Eigen functions and Eigenvalues of Lz  

5.7.2 Eigen functions of L²  

5.7.3 Properties of the Spherical Harmonics  

5.8 Solved Problems  

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