Quantum Mechanics Volume 2 Angular Momentum Spin and Approximation Methods 2nd Edition by Claude Cohen Tannoudji, Bernard Diu, Franck Laloë 9783527822737 3527822739

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ISBN 10: 3527822739
ISBN 13: 9783527822737
Author: Claude Cohen Tannoudji, Bernard Diu, Franck Laloë

This new edition of the unrivalled textbook introduces concepts such as the quantum theory of scattering by a potential, special and general cases of adding angular momenta, time-independent and time-dependent perturbation theory, and systems of identical particles. The entire book has been revised to take into account new developments in quantum mechanics curricula.

The textbook retains its typical style also in the new edition: it explains the fundamental concepts in chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications.

* The quantum mechanics classic in a new edition: written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard Diu and Franck Laloe
* As easily comprehensible as possible: all steps of the physical background and its mathematical representation are spelled out explicitly
* Comprehensive: in addition to the fundamentals themselves, the book contains more than 170 worked examples plus exercises

Claude Cohen-Tannoudji was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Superieure in Paris where he also studied and received his PhD in 1962. In 1973 he became Professor of atomic and molecular physics at the College des France. His main research interests were optical pumping, quantum optics and atom-photon interactions. In 1997, Claude Cohen-Tannoudji, together with Steven Chu and William D. Phillips, was awarded the Nobel Prize in Physics for his research on laser cooling and trapping of neutral atoms.

Bernard Diu was Professor at the Denis Diderot University (Paris VII). He was engaged in research at the Laboratory of Theoretical Physics and High Energy where his focus was on strong interactions physics and statistical mechanics.

Franck Laloe was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Superieure in Paris. His first assignment was with the University of Paris VI before he was appointed to the CNRS, the French National Research Center. His research was focused on optical pumping, statistical mechanics of quantum gases, musical acoustics and the foundations of quantum mechanics.

Quantum Mechanics Volume 2 Angular Momentum Spin and Approximation Methods 2nd Table of contents:

Chapter VIII: An elementary approach to the quantum theory of scattering by a potential

A. Introduction

B. Stationary scattering states. Calculation of the cross section

C. Scattering by a central potential. Method of partial waves

COMPLEMENTS OF CHAPTER VIII, READER’S GUIDE

Complement AVIII The free particle: stationary states with well-defined angular momentum

1. The radial equation

2. Free spherical waves

3. Relation between free spherical waves and plane waves

Complement BVIII Phenomenological description of collisions with absorption

1. Principle involved

2. Calculation of the cross sections

Complement CVIII Some simple applications of scattering theory

1. The Born approximation for a Yukawa potential

2. Low energy scattering by a hard sphere

3. Exercises

Chapter IX: Electron spin

A. Introduction of electron spin

B. Special properties of an angular momentum 1/2

C. Non-relativistic description of a spin 1/2 particle

COMPLEMENTS OF CHAPTER IX, READER’S GUIDE

Complement AIX Rotation operators for a spin 1/2 particle

1. Rotation operators in state space

2. Rotation of spin states

3. Rotation of two-component spinors

Complement BIX Exercises

Chapter X: Addition of angular momenta

A. Introduction

B. Addition of two spin 1/2’s. Elementary method

C. Addition of two arbitrary angular momenta. General method

COMPLEMENTS OF CHAPTER X, READER’S GUIDE

Complement AX Examples of addition of angular momenta

1. Addition of j1 = 1 and j2 = 1

2. Addition of an integral orbital angular momentum and a spin 1/2

Complement BX Clebsch-Gordan coefficients

1. General properties of Clebsch-Gordan coefficients

2. Phase conventions. Reality of Clebsch-Gordan coefficients

3. Some useful relations

Complement CX Addition of spherical harmonics

1. The functions ΦMJ(Ω1; Ω2)

2. The functions Fml (Ω)

3. Expansion of a product of spherical harmonics; the integral of a product of three spherical harmonics

Complement DX Vector operators: the Wigner-Eckart theorem

1. Definition of vector operators; examples

2. The Wigner-Eckart theorem for vector operators

3. Application: calculation of the Landé gJ factor of an atomic level

Complement EX Electric multipole moments

1. Definition of multipole moments

2. Matrix elements of electric multipole moments

Complement FX Two angular momenta J1 and J2 coupled by an interaction aJ1 J2

1. Classical review

2. Quantum mechanical evolution of the average values ⟨J1⟩ and ⟨J2⟩

3. The special case of two spin 1/2’s

4. Study of a simple model for the collision of two spin 1/2 particles

Complement GX Exercises

Chapter XI: Stationary perturbation theory

A. Description of the method

B. Perturbation of a non-degenerate level

C. Perturbation of a degenerate state

COMPLEMENTS OF CHAPTER XI, READER’S GUIDE

Complement AXI A one-dimensional harmonic oscillator subjected to a perturbing potential in x, x2, x3

1. Perturbation by a linear potential

2. Perturbation by a quadratic potential

3. Perturbation by a potential in x3

Complement BXI Interaction between the magnetic dipoles of two spin 1/2 particles

1. The interaction Hamiltonian W

2. Effects of the dipole-dipole interaction on the Zeeman sublevels of two fixed particles

3. Effects of the interaction in a bound state

Complement CXI Van der Waals forces

1. The electrostatic interaction Hamiltonian for two hydrogen atoms

2. Van der Waals forces between two hydrogen atoms in the 1s ground state

3. Van der Waals forces between a hydrogen atom in the 1s state and a hydrogen atom in the 2p state

4. Interaction of a hydrogen atom in the ground state with a conducting wall

Complement DXI The volume effect: the influence of the spatial extension of the nucleus on the atomic levels

1. First-order energy correction

2. Application to some hydrogen-like systems

Complement EXI The variational method

1. Principle of the method

2. Application to a simple example

3. Discussion

Complement FXI Energy bands of electrons in solids: a simple model

1. A first approach to the problem: qualitative discussion

2. A more precise study using a simple model

Complement GXI A simple example of the chemical bond: the H+2 ion

1. Introduction

2. The variational calculation of the energies

3. Critique of the preceding model. Possible improvements 1201

4. Other molecular orbitals of the H+2 ion

5. The origin of the chemical bond; the virial theorem

Complement HXI Exercises

Chapter XII: An application of perturbation theory: the fine and hyperfine structure of hydrogen

A. Introduction

B. Additional terms in the Hamiltonian

C. The fine structure of the n = 2 level

D. The hyperfine structure of the n = 1 level

E. The Zeeman effect of the 1s ground state hyperfine structure

COMPLEMENTS OF CHAPTER XII, READER’S GUIDE

Complement AXII The magnetic hyperfine Hamiltonian

1. Interaction of the electron with the scalar and vector potentials created by the proton

2. The detailed form of the hyperfine Hamiltonian

3. Conclusion: the hyperfine-structure Hamiltonian

Complement BXII Calculation of the average values of the fine-structure Hamiltonian in the 1s, 2s and 2p states

1. Calculation of ⟨1/R⟩, ⟨1/R2⟩ and ⟨1/R3⟩

2. The average values ⟨Wmv⟩

3. The average values ⟨WD⟩

4. Calculation of the coefficient ξ2p associated with WSO in the 2p level

Complement CXII The hyperfine structure and the Zeeman effect for muonium and positronium

1. The hyperfine structure of the 1s ground state

2. The Zeeman effect in the 1s ground state

Complement DXII The influence of the electronic spin on the Zeeman effect of the hydrogen resonance line

1. Introduction

2. The Zeeman diagrams of the 1s and 2s levels

3. The Zeeman diagram of the 2p level

4. The Zeeman effect of the resonance line

Complement EXII The Stark effect for the hydrogen atom

1. The Stark effect on the n = 1 level

2. The Stark effect on the n = 2 level

Chapter XIII: Approximation methods for time-dependent problems

A. Statement of the problem

B. Approximate solution of the Schrödinger equation

C. An important special case: a sinusoidal or constant perturbation

D. Random perturbation

E. Long-time behavior for a two-level atom

COMPLEMENTS OF CHAPTER XIII, READER’S GUIDE

Complement AXIII Interaction of an atom with an electromagnetic wave

1. The interaction Hamiltonian. Selection rules

2. Non-resonant excitation. Comparison with the elastically bound electron model

3. Resonant excitation. Absorption and induced emission

Complement BXIII Linear and non-linear responses of a two-level system subject to a sinusoidal perturbation

1. Description of the model

2. The approximate solution of the Bloch equations of the system

3. Discussion

4. Exercises: applications of this complement

Complement CXIII Oscillations of a system between two discrete states under the effect of a sinusoidal resonant perturbation

1. The method: secular approximation

2. Solution of the system of equations

3. Discussion

Complement DXIII Decay of a discrete state resonantly coupled to a continuum of final states

1. Statement of the problem

2. Description of the model

3. Short-time approximation. Relation to first-order perturbation theory .

4. Another approximate method for solving the Schrödinger equation

5. Discussion

Complement EXIII Time-dependent random perturbation, relaxation

1. Evolution of the density operator

2. Relaxation of an ensemble of spin 1/2’s

3. Conclusion

Complement FXIII Exercises

Chapter XIV Systems of identical particles

A. Statement of the problem

B. Permutation operators

C. The symmetrization postulate

D. Discussion

COMPLEMENTS OF CHAPTER XIV, READER’S GUIDE

Complement AXIV Many-electron atoms. Electronic configurations

1. The central-field approximation

2. Electron configurations of various elements

Complement BXIV Energy levels of the helium atom. Configurations, terms, multi-plets

1. The central-field approximation. Configurations

2. The effect of the inter-electron electrostatic repulsion: exchange energy, spectral terms

3. Fine-structure levels; multiplets

Complement CXIV Physical properties of an electron gas. Application to solids

1. Free electrons enclosed in a box

2. Electrons in solids

Complement DXIV Exercises

Appendix I: Fourier series and Fourier transforms

1. Fourier series

2. Fourier transforms

Appendix II: The Dirac δ-”function”

1. Introduction; principal properties

2. The -”function” and the Fourier transform

3. Integral and derivatives of the δ-”function”

4. The δ-”function” in three-dimensional space

Appendix III: Lagrangian and Hamiltonian in classical mechanics

1. Review of Newton’s laws

2. The Lagrangian and Lagrange’s equations

3. The classical Hamiltonian and the canonical equations

4. Applications of the Hamiltonian formalism

5. The principle of least action

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