Lectures on Quantum Mechanics Book

Preface     xv
Praise of physics     1
The interplay of the eye and the mind     1
Advanced technologies     5
The pillars of contemporary physics     6
Mysteries of light     6
Fundamental structure of matter     8
The infinitely complex     9
The Universe     12
A quantum phenomenon     13
Wave behavior of particles     16
Interferences     16
Wave behavior of matter     17
Analysis of the phenomenon     18
Probabilistic nature of quantum phenomena     20
Random behavior of particles     20
A nonclassical probabilistic phenomenon     20
Conclusions     21
Phenomenological description     23
Wave function, Schrodinger equation     25
Terminology and methodology     25
Terminology     25
Methodology     26
Principles of wave mechanics     27
The interference experiment     27
Wave function     27
Schrodinger equation     29
Superposition principle     30
Wave packets     31
Free wavepackets     31
Fourier transformation     32
Shape of wave packets     33
Historical landmarks     33
Momentum probability law     35
Free particle     35
General case     36
Heisenberg uncertainty relations     36
Size and energy of a quantum system     37
Stability of matter     38
Controversies and paradoxes     40
The 1927 Solvay Congress     40
The EPR paradox     41
Hidden variables, Bell's inequalities     41
The experimental test     42
Physical quantities     45
Statement of the problem     46
Physical quantities     46
Position and momentum     47
Observables     48
Position observable     49
Momentum observable     49
Correspondence principle     50
Historical landmarks     50
A counterexample of Einstein and its consequences     51
What do we know after a measurement?     53
Eigenstates and eigenvalues of an observable     54
Wave packet reduction     55
The specific role of energy      56
The Hamiltonian     56
The Schrodinger equation, time and energy     57
Stationary states     58
Motion: Interference of stationary states     59
Schrodinger's cat     60
The dreadful idea     60
The classical world     63
Energy quantization     65
Methodology     65
Bound states and scattering states     66
One-dimensional problems     67
The harmonic oscillator     67
Harmonic potential     67
Energy levels, eigenfunctions     68
Square well potentials     69
Square potentials     69
Symmetric square well     70
Infinite well, particle in a box     73
Double well, the ammonia molecule     74
The model     74
Stationary states, the tunnel effect     75
Energy levels     76
Wave functions     78
Inversion of the molecule     79
Illustrations and applications of the tunnel effect     81
Sensitivity to the parameters     81
Molecular structure     82
Tunneling microscopy, nanotechnologies     84
Nanotechnologies      84
Classical limit     85
Principles of quantum mechanics     87
Hilbert space     88
Two-dimensional space     89
Square integrable functions     89
Dirac formalism     92
Notations     92
Operators     93
Syntax rules     95
Projectors; decomposition of the identity     95
Measurement results     96
Eigenvectors and eigenvalues of an observable     96
Results of the measurement of a physical quantity     97
Probabilities     98
The Riesz spectral theorem     98
Physical meaning of various representations     100
Principles of quantum mechanics     101
The principles     101
The case of a continuous spectrum     102
Interest of this synthetic formulation     102
Heisenberg's matrices     103
Matrix representation of operators     103
Matrices X and P     104
Heisenberg's thoughts     104
The polarization of light, quantum "logic"     107
Two-state systems     113
The NH[subscript 3] molecule     113
"Two-state" system      114
Matrix quantum mechanics     116
Vectors     116
Hamiltonian     117
Observables     117
Examples     119
Basis of classical configurations     119
Interference and measurement     120
NH[subscript 3] in an electric field     120
Uniform constant field     121
Weak and strong field regimes     122
Other two-state systems     123
The ammonia molecule in an inhomogeneous field     123
Force on the molecule in an inhomogeneous field     124
Population inversion     126
Reaction to an oscillating field, the maser     126
Principle and applications of the maser     128
Amplifiers     129
Oscillators     130
Atomic clocks     130
Tests of relativity     132
Neutrino oscillations     134
Lepton families     134
Mechanism of the oscillations; reactor neutrinos     135
Successive hermaphroditism of neutrinos     138
Algebra of observables     143
Commutation of observables     143
Fundamental commutation relation     143
Other commutation relations     144
Dirac in the summer of 1925     145
Uncertainty relations     146
Evolution of physical quantities     147
Evolution of an expectation value     147
Particle in a potential, classical limit     148
Conservation laws     149
Algebraic resolution of the harmonic oscillator     150
Operators a, a, and N     151
Determination of the eigenvalues     151
Eigenstates     152
Commuting observables     154
Theorem     154
Example     155
Tensor structure of quantum mechanics     155
Complete set of commuting observables (CSCO)     156
Completely prepared quantum state     157
Sunday, September 20, 1925     158
Angular momentum     161
Fundamental commutation relation     162
Classical angular momentum     162
Definition of an angular momentum observable     162
Results of the quantization     163
Proof of the quantization     163
Statement of the problem     163
Vectors |j, m > and eigenvalues j and m     164
Operators J[Characters not reproducible] = J[subscript x Characters not reproducible] iJ[subscript y]     165
Quantization     166
Orbital angular momenta     168
Formulae in spherical coordinates     168
Integer values of m and l     168
Spherical harmonics     169
Rotation energy of a diatomic molecule     170
Diatomic molecule     171
The CO molecule     172
Angular momentum and magnetic moment     173
Classical model     173
Quantum transposition     175
Experimental consequences     175
Larmor precession     176
What about half-integer values of j and m?     177
The Hydrogen Atom     179
Two-body problem; relative motion     180
Motion in a central potential     182
Spherical coordinates, CSCO     182
Eigenfunctions common to H, L[superscript 2], and L[subscript z]     182
Quantum numbers     183
The hydrogen atom     186
Atomic units; fine structure constant     186
The dimensionless radial equation     188
Spectrum of hydrogen     191
Stationary states of the hydrogen atom     191
Dimensions and orders of magnitude      193
Historical landmarks     194
Muonic atoms     195
Spin 1/2     199
Experimental results     199
Spin 1/2 formalism     200
Representation in a particular basis     201
Matrix representation     201
Complete description of a spin 1/2 particle     202
Observables     203
Physical spin effects     204
Spin magnetic moment     205
Hamiltonian of a one-electron atom     205
The Stern-Gerlach experiment     206
Principle of the experiment     206
Semi-classical analysis     207
Experimental results     208
Explanation of the Stern-Gerlach experiment     208
Successive Stern-Gerlach setups     211
Measurement along an arbitrary axis     211
The discovery of spin     213
The hidden sides of the Stern-Gerlach experiment     213
Einstein and Ehrenfest's objections     215
Anomalous Zeeman effect     216
Bohr's challenge to Pauli     217
The spin hypothesis     217
The fine structure of atomic lines     218
Magnetism, magnetic resonance     219
Spin effects, Larmor precession     220
Larmor precession in a fixed magnetic field     221
Rabi's calculation and experiment     221
Nuclear magnetic resonance     225
Magnetic moments of elementary particles     227
Entertainment: Rotation by 2[pi] of a spin 1/2     228
The Pauli Principle     229
Indistinguishability of two identical particles     230
Identical particles in classical physics     230
The quantum problem     230
Example of ambiguities     231
Systems of two spin 1/2 particles, total spin     232
The Hilbert space of the problem     232
Hilbert space of spin variables     232
Matrix representation     233
Total spin states     233
Two-particle system; the exchange operator     235
The Hilbert space for the two-particle system     235
The exchange operator between identical particles     236
Symmetry of the states     237
The Pauli principle     238
The case of two particles     238
Independent fermions and exclusion principle     239
The case of N identical particles     239
Physical consequences of the Pauli principle      241
Exchange force between two fermions     241
The ground state of N identical independent particles     241
Behavior of fermion and boson systems at low temperatures     243
Entangled states: The way of paradoxes     247
The EPR paradox     247
The version of David Bohm     249
Bell's inequality     251
Experimental tests     254
Quantum cryptography; how to enjoy a nuisance     256
The communication between Alice and Bob     256
Present experimental setups     258
Quantum teleportation     260
Bell states     260
Teleportation     261
Quantum mechanics in the Universe     263
Quantum mechanics and astronomy     265
Life and death of stars     265
Spectroscopy     268
Radioastronomy, the interstellar medium     268
The interstellar medium     269
Cosmic background radiation: Birth of the Universe     273
The 21-cm line of hydrogen     275
Hyperfine structure of hydrogen     276
Hydrogen maser     278
Importance of the 21-cm line     279
The Milky Way     280
The intergalactic medium; star wars     281
Spiral arms, birthplaces of stars     285
Interstellar molecules, the origin of life     287
Rotation spectra of molecules     287
Interstellar molecules     288
The origin of life     289
Where are they? Quantum mechanics, the universal cosmic language     291
Life, intelligence, and thought     291
Listening to extraterrestrials     293
Quantum mechanics, the universal cosmic language     295
Index     303