Introduction to the Quantum Theory (2nd Ed) - David Park

PART I THEORY.................................................. 17 1 The Inadequacy of Classical Physics.......................... 19 1.1 The wave nature of hght................................ 19 1.2 The particle nature of light........................... 22 1.3 The behavior of electrons.............................. 26 1.4 The wave theory of matter.............................. 33 1.5 The principle of superposition......................... 38 2 The Physical Content of the Wave Function.................... 44 2.1 The wave function of an electron....................... 44 2.2 The wave function of a photon.......................... 48 2.3 Expectation values, probabilities and superposition.... 50 2.4 rrhe momentum wave function............................ 55 2.5 The momentum operator.................................. 57 2.6 Indeterminacy.......................................... 63 3 General Principles........................................... 76 3.1 Interactions........................................... 76 3.2 The current vector..................................... 78 3.3 Time dependence of expectation values.................. 80 3.4 Hermitian operators.................................... 86 3.5 The indeterminacy relations............................ 91 3.6 Eigenstates............................................ 95 3.7 Superpositions.........................................100 3.8 Summary................................................103 4 Systems in One Dimension.....................................105 4.1 Simple barriers........................................105 4.2 Potential wells........................................112 4.3 Classical considerations on 1/1........................118 4.4 The WKB approximation..................................120 4.5 The connection formulas................................124 4.6 The anharmonic oscillator..............................131 4.7 The double potential well..............................132 4.8 The harmonic oscillator................................139 4.9 Analytical solution....................................139 4.10 Algebraic solution....................................143 5 Hermitian Operators, Symmetry, and Angular Momentum..........151 5.1 The orthogonality theorem..............................151 5.2 Eigenfunction expansions...............................153 5.3 Matrices and the Dirac notation........................156 5.4 Simultaneous observables...............................159 5.5 Transformations as dynamical variables.................162 5.6 Hermitian momenta in curvilinear coordinates...........172 5.7 Angular momentum.......................................173 5.8 The eigenvalues of Lz and L 2..........................179 5.9 Note on infinitesimal transformations..................183 6 Spin and Isospin.............................................186 6.1 The phenomenon of spin.................................186 6.2 Spin in a constant magnetic field......................194 6.3 Magnetic resonance.....................................198 6.4 Addition of two spins..................................201 6.5 Addition of spin and orbital angular momenta...........205 6.6 Isospin................................................212 6.7 Isospin and elementary particles.......................217 7 Systems in Two and Three Dimensions..........................223 7.1 Degeneracy.............................................223 7.2 Systems of several particles...........................233 7.3 The hydrogen atom......................................237 7.4 A singular potential...................................247 7.5 The deuteron...........................................250 7..6 The diatomic molecule.................................259 7.7 Electron in a magnetic field...........................263

7.8 Fields or potentials...................................271 7.9 Superconductivity and quantized flux...................276 8 Approximate Methods of Calculation...........................278 8.1 Introduction...........................................278 8.2 Perturbation theory for stationary states..............278 8.3 First-order perturbations..............................282 8.4 Perturbation of degenerate states......................285 8.5 Calculation of perturbed wave functions................298 8.6 The variation principle................................305 8.7 Perturbation theory for nonstationary states...........310 8.8 Perturbations periodic in time.........................322 8.9 Electric and magnetic moments..........................324 9 The Theory of Scattering.....................................329 9.1 The scattering cross section...........................330 9.2 Coordinate systems.....................................333 9.3 The quantum theory of scattering: I....................339 9.4 The quantum theory of scattering: II...................348 9.5 Formation of cloud chamber tracks......................359 9.6 Low-energy scattering..................................362 9.7 Short-range interactions...............................370 9.8 The Heisenberg..Kramers approach.......................377 9.9 Resonant scattering....................................381 10 Electromagnetic Radiation...................................389 10.1 Interaction with an electromagnetic field.............389 10.2 Dipole radiation......................................393 10.3 Spectral lines........................................397 10.4 Selection rules and forbid den transitions............404 10.5 Photoelectric effect..................................414 11 Systems Containing Identical Particles......................419 11.1 Symmetry and antisymmetry.............................419 11.2 The helium spectrum...................................427 11.3 Antisymmetrical wave functions........................432 11.4 Scattering of identical particles.....................435 11.5 Photon statistics.....................................441 11.6 Neutrons and protons..................................445 Part II APPLICATIONS...........................................447 12 The Theory of Alpha Decay...................................449 12.1 The escape of an alpha particle.......................449 12.2 Evaluation of the formula.............................454 13 Electrons in a Periodic Lattice.............................458 13.1 The periodic potential................................458 13.2 Effective mass........................................463 13.3 Electronic conductivity in solids.....................466 14 The Hydrogen Atom...........................................471 14.1 The wave equation.....................................471 14.2 Solution of the equation..............................473 14.3 The fine structure of hydrogen........................479 14.4 The Zeeman effect.....................................488 15 The Helium Atom.............................................495 15.1 The ground state......................................496 15.2 The lowest excited states.............................505 15.3 Nuclear motion in helium..............................508 16 Interatomic Forces..........................................512 16.1 The hydrogen molecule-ion.............................512 16.2 The mechanics of a molecule...........................521 16.3 Forces in molecules...................................523 16.4 Forces between atoms..................................524 17 The Quark Model of the Baryons..............................529 17..1 Elements of the model................................529 17..2 Classification of baryon states......................532

17.3 The masses of the baryon multiplets...................533 17.4 Magnetic moments......................................537 17.5 Mass differences within a mUltiplet...................538 18 The Neutron-Proton Interaction..............................540 18.1 The bound state.......................................541 18.2 Neutron-proton sea ttering............................542 18.3 Scattering of neutrons by H 2.........................547 18.4 The photodissociation of the deuteron.................551 19 Thermodynamics..............................................558 19.1 Thermodynamical questions.............................558 19.2 Ensembles.............................................559 19.3 The Boltzmann distribution............................567 19.4 Work and heat.........................................578 20 Statistical Quantum Mechan ics..............................583 20.1 The micro canonical ensemble..........................584 20.2 The entropy...........................................588 20.3 Photons and phonons...................................595 20.4 A gas of permanent bosons.............................603 20.5 Liquid helium.........................................610 20.6 A gas of fermions.....................................612 20.7 Electrons in a metal..................................619 APPENDIXES.....................................................629 1. Complex numbers.............................................629 2. Fourier integrals and completeness relations................634