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From the Preface to the first English edition xi
Preface to the second English edition xii
Preface to the third Russian edition xiii
Editor's Preface to the fourth Russian edition xiv
Notation xv
I. THE BASIC CONCEPTS OF QUANTUM MECHANICS
The uncertainty principle 1 (5)
The principle of superposition 6 (2)
Operators 8 (5)
Addition and multiplication of operators 13 (2)
The continuous spectrum 15 (4)
The passage to the limiting case of classical 19 (2)
mechanics
The wave function and measurements 21 (4)
II. ENERGY AND MOMENTUM
The Hamiltonian operator 25 (1)
The differentiation of operators with respect 26 (1)
to time
Stationary states 27 (3)
Matrices 30 (5)
Transformation of matrices 35 (2)
The Heisenberg representation of operators 37 (1)
The density matrix 38 (3)
Momentum 41 (4)
Uncertainty relations 45 (5)
III. SCHRODINGER'S EQUATION
Schrodinger's equation 50 (3)
The fundamental properties of Schrodinger's 53 (2)
equation
The current density 55 (3)
The variational principle 58 (2)
General properties of motion in one dimension 60 (3)
The potential well 63 (4)
The linear oscillator 67 (7)
Motion in a homogeneous field 74 (2)
The transmission coefficient 76 (6)
IV. ANGULAR MOMENTUM
Angular momentum 82 (4)
Eigenvalues of the angular momentum 86 (3)
Eigenfunctions of the angular momentum 89 (3)
Matrix elements of vectors 92 (4)
Parity of a state 96 (3)
Addition of angular momenta 99 (3)
V. MOTION IN A CENTRALLY SYMMETRIC FIELD
Motion in a centrally symmetric field 102 (3)
Spherical waves 105 (7)
Resolution of a plane wave 112 (2)
Fall of a particle to the centre 114 (3)
Motion in a Coulomb field (spherical polar 117 (12)
coordinates)
Motion in a Coulomb field (parabolic 129 (4)
coordinates)
VI. PERTURBATION THEORY
Perturbations independent of time 133 (5)
The secular equation 138 (4)
Perturbations depending on time 142 (4)
Transitions under a perturbation acting for a 146 (5)
finite time
Transitions under the action of a periodic 151 (3)
perturbation
Transitions in the continuous spectrum 154 (3)
The uncertainty relation for energy 157 (2)
Potential energy as a perturbation 159 (5)
VII. THE QUASI-CLASSICAL CASE
The wave function in the quasi-classical case 164 (3)
Boundary conditions in the quasi-classical 167 (3)
case
Bohr and Sommerfeld's quantization rule 170 (5)
Quasi-classical motion in a centrally 175 (4)
symmetric field
Penetration through a potential barrier 179 (6)
Calculation of the quasi-classical matrix 185 (6)
elements
The transition probability in the 191 (4)
quasi-classical case
Transitions under the action of adiabatic 195 (4)
perturbations
VIII. SPIN
Spin 199 (4)
The spin operator 203 (3)
Spinors 206 (4)
The wave functions of particles with 210 (5)
arbitrary spin
The operator of finite rotations 215 (6)
Partial polarization of particles 221 (2)
Time reversal and Kramers' theorem 223 (4)
IX. IDENTITY OF PARTICLES
The principle of indistinguishability of 227 (3)
similar particles
Exchange interaction 230 (4)
Symmetry with respect to interchange 234 (7)
Second quantization. The case of Bose 241 (6)
statistics
Second quantization. The case of Fermi 247 (4)
statistics
X. THE ATOM
Atomic energy levels 251 (1)
Electron states in the atom 252 (4)
Hydrogen-like energy levels 256 (1)
The self-consistent field 257 (4)
The Thomas-Fermi equation 261 (5)
Wave functions of the outer electrons near 266 (1)
the nucleus
Fine structure of atomic levels 267 (4)
The Mendeleev periodic system 271 (8)
X-ray terms 279 (2)
Multipole moments 281 (3)
An atom in an electric field 284 (5)
A hydrogen atom in an electric field 289 (11)
XI. THE DIATOMIC MOLECULE
Electron terms in the diatomic molecule 300 (2)
The intersection of electron terms 302 (3)
The relation between molecular and atomic 305 (4)
terms
Valency 309 (7)
Vibrational and rotational structures of 316 (5)
singlet terms in the diatomic molecule
Multiplet terms. Case a 321 (4)
Multiplet terms. Case b 325 (4)
Multiplet terms. Cases c and d 329 (2)
Symmetry of molecular terms 331 (3)
Matrix elements for the diatomic molecule 334 (4)
A-doubling 338 (3)
The interaction of atoms at large distances 341 (3)
Pre-dissociation 344 (12)
XII. THE THEORY OF SYMMETRY
Symmetry transformations 356 (3)
Transformation groups 359 (3)
Point groups 362 (8)
Representations of groups 370 (8)
Irreducible representations of point groups 378 (4)
Irreducible representations and the 382 (3)
classification of terms
Selection rules for matrix elements 385 (4)
Continuous groups 389 (4)
Two-valued representations of finite point 393 (5)
groups
XIII. POLYATOMIC MOLECULES
The classification of molecular vibrations 398 (7)
Vibrational energy levels 405 (2)
Stability of symmetrical configurations of 407 (5)
the molecule
Quantization of the rotation of a top 412 (9)
The interaction between the vibrations and 421 (4)
the rotation of the molecule
The classification of molecular terms 425 (8)
XIV. ADDITION OF ANGULAR MOMENTA
3j-symbols 433 (8)
Matrix elements of tensors 441 (3)
6j-symbols 444 (6)
Matrix elements for addition of angular 450 (2)
momenta
Matrix elements for axially symmetric systems 452 (3)
XV. MOTION IN A MAGNETIC FIELD
Schrodinger's equation in a magnetic field 455 (3)
Motion in a uniform magnetic field 458 (5)
An atom in a magnetic field 463 (7)
Spin in a variable magnetic field 470 (2)
The current density in a magnetic field 472 (2)
XVI. NUCLEAR STRUCTURE
Isotopic invariance 474 (4)
Nuclear forces 478 (4)
The shell model 482 (9)
Non-spherical nuclei 491 (5)
Isotopic shift 496 (2)
Hyperfine structure of atomic levels 498 (3)
Hyperfine structure of molecular levels 501 (3)
XVII. ELASTIC COLLISIONS
The general theory of scattering 504 (4)
An investigation of the general formula 508 (3)
The unitarity condition for scattering 511 (4)
Born's formula 515 (6)
The quasi-classical case 521 (5)
Analytical properties of the scattering 526 (6)
amplitude
The dispersion relation 532 (3)
The scattering amplitude in the momentum 535 (3)
representation
Scattering at high energies 538 (7)
The scattering of slow particles 545 (7)
Resonance scattering at low energies 552 (7)
Resonance at a quasi-discrete level 559 (5)
Rutherford's formula 564 (3)
The system of wave functions of the 567 (4)
continuous spectrum
Collisions of like particles 571 (3)
Resonance scattering of charged particles 574 (5)
Elastic collisions between fast electrons and 579 (4)
atoms
Scattering with spin-orbit interaction 583 (6)
Regge poles 589 (6)
XVIII. INELASTIC COLLISIONS
Elastic scattering in the presence of 595 (6)
inelastic processes
Inelastic scattering of slow particles 601 (2)
The scattering matrix in the presence of 603 (4)
reactions
Breit and Wigner's formulae 607 (8)
Interaction in the final state in reactions 615 (3)
Behaviour of cross-sections near the reaction 618 (6)
threshold
Inelastic collisions between fast electrons 624 (9)
and atoms
The effective retardation 633 (4)
Inelastic collisions between heavy particles 637 (3)
and atoms
Scattering of neutrons 640 (4)
Inelastic scattering at high energies 644 (27)
MATHEMATICAL APPENDICES
a. Hermite polynomials 651 (3)
b. The Airy function 654 (2)
c. Legendre polynomials 656 (3)
d. The confluent hypergeometric function 659 (4)
e. The hypergeometric function 663 (3)
f. The calculation of integrals containing 666 (5)
confluent hypergeometric functions
Index 671

This edition has been completely revised to include some 20% of new material. Important recent developments such as the theory of Regge poles are now included. Many problems with solutions have been added to those already contained in the book.