DeutschesFachbuch.de : Quantum Physics Von Florian Scheck

INHALTSVERZEICHNIS | öffnen

Table of Contents
PART ONE
From the Uncertainty Relation to Many-Body Systems
1.Quantum Mechanics of Point Particles
1.1 Limitations of Classical Physics 4
1.2 Heisenberg's Uncertainty Relation for Position and Momentum 16
1.2.2 Uncertainties of Observables 17
1.2.3 Quantum Mechanical Uncertainties of Canonically Conjugate Variables 20
1.2.3 Examples for Heisenberg's Uncertainty Relation 24
1.3 The Particle-Wave Dualism 26
1.3.1 The Wave Function and its Interpretation 28
1.3.2 A First Link to Classical Mechanics 31
1.3.3 Gaussian Wave Packet 32
1.3.4 Electron in External Electromagnetic Fields 35
1.4 Schrödinger Equation and Born's Interpretation of the Wave Function 39
1.5 Expectation Values and Observables 45
1.5.1 Observables as Self-Adjoint Operators on L 2(R 3)47
1.5.2 Ehrenfest's Theorem 50
1.6 A Discrete Spectrum: Harmonic Oscillator in one Dimension. 53
1.7 Orthogonal Polynomials in One Real Variable 65
1.8 Observables and Expectation Values 72
1.8.1 Observables With Nondegenerate Spectrum 72
1.8.2 An Example: Coherent States 77
1.8.3 Observables with Degenerate, Discrete Spectrum 81
1.8.4 Observables with Purely Continuous Spectrum 86
1.9 Central Forces and the Schrödinger Equation 91
1.9.1 The Orbital Angular Momentum: Eigenvalues and Eigenfunctions 91
1.9.2 Radial Momentum and Kinetic Energy 101
1.9.3 Force Free Motion with Sharp Angular Momentum 104
1.9.4 The Spherical Oscillator 111
1.9.5 Mixed Spectrum: The Hydrogen Atom 118
2.Scattering of Particles by Potentials
2.1 Macroscopic and Microscopic Scales 129
2.2 Scattering on a Central Potential 131
2.2 Partial Wave Analysis 136
2.3.1 How to Calculate Scattering Phases 140
2.3.2 Potentials with Infinite Range: Coulomb Potential 144
2.4 Born Series and Born Approximation 147
2.4.1 First Born Approximation 150
2.4.2 Form Factors in Elastic Scattering 152
2.5* Analytical Properties of Partial Wave Amplitudes 156
2.5.1 Jost Functions 157
2.5.2 Dynamic and Kinematic Cuts 158
2.5.3 Partial Wave Amplitudes as Analytic Functions 161
2.5.4 Resonances 161
2.5.5 Scattering Length and Effective Range 164
2.6 Inelastic Scattering and Partial Wave Analysis 167
3.The Principles of Quantum Theory
3.1 Representation Theory 171
3.1.1 Dirac's Bracket Notation 174
3.1.2 Transformations Relating Different Representations 177
3.2 The Concept of Hilbert Space 180
3.2.1 Definition of Hilbert Spaces 182
3.2.2 Subspaces of Hilbert Spaces 187
3.2.3 Dual Space of a Hilbert Space and Dirac's Notation 188
3.3 Linear Operators on Hilbert Spaces 190
3.3.1 Self-Adjoint Operators 191
3.3.2 Projection Operators 194
3.3.3 Spectral Theory of Observables 196
3.3.4 Unitary Operators 200
3.3.5 Time Evolution of Quantum Systems 202
[weiter lesen]

REGISTER | öffnen

Subject Index
AAbsorption 169
Action 6
Addition of angular momenta 351
Addition theorem
- for spherical harmonics 98
Algebra
- graded 517
Angular momentum -orbital 91
Annihilation operators
- for fermions 536
Annihilation operators
- for photons 443
Anomalous magnetic moment
- Schwinger 622
Anomaly
- of g-f actor 610
Anticommutator 517
Antihermitean 228
Anti-isomorphism 189
Antiparticle 256, 523
- with spin 0 428
Antiunitary operators 252
BBaryon number 330
Baryons 380
Base vectors
- in R 4 390
Basis
- spherical 291, 445
Bessel functions 144
- spherical 106
Bessel's differential equation 105
Bhabha scattering 585
Bit
- classical 281
- quantum 282
Bogoliubov's method for pairing forces 322
Bohr magneton 240, 680
Bohr radius 7, 680
Born approximation 147
- first 150
Born series 147, 149
Born's interpretation 39
- of wave function 41
Bose-Einstein condensation 268
Bose-Einstein statistics 268
Bosons 266
Boundary condition
- of Schrödinger 44
- of Born 44
- de Broglie-wave length 27
Cc-number 411
Campbell-Hausdorff formula 222
- Canonical Momentum
- for Maxwell field 436
Casimir operators 378
Cauchy series 183
Center-of-mass system
- in scattering 492
Central forces 91
Channels 167
Characteristic exponent
- in DE of Fuchsian type 105
Charge conjugation 256, 333
- Dirac field 527
Charge operator
- for fermions 537
Charged current 641
Chiral Fields 553
Circular orbit 700
Clebsch-Gordan coefficients 242, 244
- being real 355
- symmetry relations 357
Clebsch-Gordan series 242
Clifford algebra 516
Coherent state 79, 705
Colliding beam 492
Completeness 73, 89, 90
- asymptotic 485
- of description 329
- of hydrogen functions 127
- of spherical harmonics 97
Completeness of functions 69
Completeness relation 176
Compton-Effekt 585
Condon-Shortley phase convention 101, 236
Confluent hypergeometric function 114, 664
Contact interaction 642
Continuity equation 38
Contraction 318
contragredient 352
Coordinates
- parabolic 145
- spherical 228
Correlation function
two-body 274
Correspondence principle 9
- Cosets 338
Coulomb interaction
- instantaneous 440
Coulomb phase 125, 147
Coulomb potential 132
Coupling
- minimal 429
Coupling constant
- running 635
Creation operators
- for fermions 536
Creation operators
- for photons 443
Cross section -differential 133
- integrated elastic 134
- Rutherford 497 -total 140, 167
Crossing 587
Current
charged 557
Current density
- for complex scalar field 428
Cut
- dynamic 158
- kinematic 158, 160
- left 159
DD-functions
- basis in Eulerian angles 348
- completeness 348
- orthogonality 344
- symmetry relations 343
dagger 191
Decay
- π0 -> 2 γ 499
- in 2 particles 498
- in 3 particles 500
- of η -meson in lepton pair 557
- of muon 644
- of pions 256
- of the π 649
Density 65
- one-body 272
- two-body 273
Density matrix 208
- for neutrinos/antineutrinos 544
Deviation
- mean square 19
- standard 19
Differential equation
- Fuchsian type 96
- of Kummer 113
Diffraction minima 156
Dirac equation
- in momentum space 515
- in polar coordinates 560
- in spacetime 525
Dirac's bracket notation 174
Dirac's δ -distribution 653, 658
Dirac's operator 561
Discrete spectrum 53
Dispersion
- of wave packet 35
Dispersion relation 29
Distribution
- acausal 424
- tempered 87, 653
Distribution
- causal for mass m 420
Dual space of H 188, 189
Dualism
- particle-wave 26
Dyson series 304, 575
EEffective range 166
Ehrenfest's theorem 50, 52
Eigenfunction 72
Eigenspace 194
Eigenvalue 72, 194
Eigenvalues
- relativistic H-Atom 568
Einstein-Planck relation 26
Electron radius
- classical 460
Elementary charge 680
Emission
- induced 452
- spontaneous 452
Energ density
- for Dirac field 538
Energy-momentum 387 - tensor field 412, 435
Energy-momentum tensor field
- for fermions 538
Ensemble
- mixed 208
Entangled state 273
Equations of motion
- Heisenberg' s 51, 413
Euler angles 236
Evolution
- time 202
Exchange interaction 310
Exchange symmetry 266
Exclusion principle 267
Expectation value 45, 46
FFactor group 338
[weiter lesen]