Quantum Mechanics

Volume II: Angular Momentum, Spin, and Approximation Methods
3. Auflage 2026
ISBN: 978-3-527-41466-6
Verlag: Wiley-VCH GmbH

Buch, Englisch, 704 Seiten, Format (B × H): 170 mm x 244 mm

Volume II of the unrivalled textbook contains the quantum theory of scattering by a potential, addition of angular momenta, time-independent and time-dependent perturbation theory, and systems of identical particles. The new edition also includes a new complement in order to treat an important subject that was missing in the previous editions: the linear response theory, very often used in many fields of physics such as atomic physics and quantum optics, condensed matter physics, and nuclear physics.

The textbook retains its typical style also in the third 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: written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard Diu and Franck Laloë
- 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

Autoren/Hrsg.

Cohen-Tannoudji, Claude

Diu, Bernard

Laloë, Franck

Weitere Mitwirkende

Ostrowsky, Nicole

Ostrowsky, Daniel

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Chemie Physikalische Chemie Quantenchemie, Theoretische Chemie
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

Volume I

I Waves and Particles. Introduction to the Basic Ideas of Quantum Mechanics 1

Reader’s Guide for Complements 33

AI Order of magnitude of the wavelengths associated with material particles 35

BI Constraints imposed by the uncertainty relations 39

CI Heisenberg relation and atomic parameters 41

DI An experiment illustrating the Heisenberg relations 45

EI A simple treatment of a two-dimensional wave packet 49

FI The relationship between one- and three-dimensional problems 53

GI One-dimensional Gaussian wave packet: spreading of the wave packet 57

HI Stationary states of a particle in one-dimensional square potentials 63

JI Behavior of a wave packet at a potential step 75

KI Exercises 83

II the Mathematical Tools of Quantum Mechanics 87

Reader’s Guide for Complements 159

AII The Schwarz inequality 161

BII Review of some useful properties of linear operators 163

CII Unitary Operators 173

DII a More Detailed Study of the R and P Representations 181

Eii Some general properties of two observables, Q and P, whose commutator is equal to ih 187

FII The parity operator 193

GII An application of the properties of the tensor product: the two dimensional infinite well 201

HII Exercises 205

III the Postulates of Quantum Mechanics 213

Reader’s Guide for Complements 267

AIII Particle in an infinite one-dimensional potential well 271

BIII Study of the probability current in some special cases 283

CIII Root Mean Square Deviations of Two Conjugate Observables 289

DIII Measurements Bearing on Only One Part of a Physical System 293

EIII The density operator 299

FIII The evolution operator 313

GIII The Schrödinger and Heisenberg pictures 317

HIII Gauge invariance 321

JIII Propagator for the Schrödinger equation 335

KIII Unstable states. Lifetime 343

LIII Exercises 347

MIII Bound States in a “potential Well” of Arbitrary Shape 359

Niii Unbound states of a particle in the presence of a potential well or barrier 367

Oiii Quantum properties of a particle in a one-dimensional periodic structure 375

IV Applications of the Postulates to Simple Cases: Spin 1/2 and Two-level Systems 393

Reader’s Guide for Complements 423

AIV The Pauli matrices 425

BIV Diagonalization of a 2 × 2 Hermitian matrix 429

CIV Fictitious Spin 1/2 Associated with a Two-level System 435

DIV System of Two Spin 1/2 Particles 441

EIV Spin 1/2 Density Matrix 449

FIV Spin 1/2 Particle in a Static and a Rotating Magnetic field: Magnetic Resonance 455

GIV a Simple Model of the Ammonia Molecule 469

HIV Effects of a Coupling Between a Stable State and An Unstable State 485

JIV Exercises 491

V the One-dimensional Harmonic Oscillator 497

Reader’s Guide for Complements 525

AV Some Examples of Harmonic Oscillators 527

Bv Study of the Stationary States in the X Representation. Hermite Polynomials 547

Cv Solving the eigenvalue equation of the harmonic oscillator by the polynomial method 555

DV Study of the Stationary States in the Momentum Representation 563

EV the Isotropic Three-dimensional Harmonic Oscillator 569

FV a Charged Harmonic Oscillator in a Uniform Electric field 575

GV Coherent “quasi-classical” States of the Harmonic Oscillator 583

HV Normal Vibrational Modes of Two Coupled Harmonic Oscillators 599

JV Vibrational Modes of An Infinite Linear Chain of Coupled Harmonic Oscillators; Phonons 611

KV Vibrational modes of a continuous physical system. Photons 631

LV One-dimensional Harmonic Oscillator in Thermodynamic Equilibrium at a Temperature T 647

MV Exercises 661

VI General Properties of Angular Momentum in Quan- Tum Mechanics 667

Reader’s Guide for Complements 703

AVI Spherical harmonics 705

BVI Angular momentum and rotations 717

CVI Rotation of Diatomic Molecules 739

DVI Angular Momentum of Stationary States of a Two-dimensional Harmonic Oscillator 755

EVI A charged particle in a magnetic field: Landau levels 771

FVI Exercises 795

VII Particle in a Central Potential, Hydrogen Atom 803

Reader’s Guide for Complements 831

AVII Hydrogen-like systems 833

BVII A soluble example of a central potential: The isotropic three-dimensional harmonic oscillator 841

CVII Probability Currents Associated with the Stationary States of the Hydrogen Atom 851

DVII the Hydrogen Atom Placed in a Uniform Magnetic field. Paramagnetism and Diamagnetism. The Zeeman Effect 855

EVII Some atomic orbitals. Hybrid orbitals 869

FVII Vibrational-rotational levels of diatomic molecules 885

GVII Exercises 899

Index 901

Über Autor(innen)

Claude Cohen-Tannoudji is a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris where he also studied and received his PhD in 1962. In 1973 he became Professor of atomic and molecular physics at the Collège 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 (1935-2025) 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 Laloë is a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure 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.