Volume I
I Waves and Particles. Introduction to the Basic Ideas of Quantum Mechanics 1
Readerâs 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
Readerâs 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 iħ 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
Readerâs 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 Schr¶dinger and Heisenberg pictures 317
HIII Gauge invariance 321
JIII Propagator for the Schr¶dinger equation 335
KIII Unstable states. Lifetime 343
LIII Exercises 347
MIII Bound States in a âpotential Wellâ 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
Readerâs 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
Readerâs 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 âquasi-classicalâ 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
Readerâs 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
Readerâs 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
