Lectures on quantum mechanics / Jean-Louis Basdevant.

Format:

Book

Author/Creator:

Basdevant, J. L. (Jean-Louis)

Language:

English

Subjects (All):

Quantum theory.

Physical Description:

xvi, 307 pages : illustrations ; 24 cm

Place of Publication:

New York : Springer, . 2007.

Summary:

Beautifully illustrated and engagingly written, Lectures on Quantum Mechanics presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk classroom lecture that students can follow with ease and enjoyment. Here is a sample of the book's style, from the opening of Chapter 1: "If one were to ask a passer-by to quote a great formula of physics, chances are that the answer would be 'E = mc[superscript 2]'. Nevertheless, the formula 'E = hv' which was written in the same year 1905 by the same Albert Einstein, and which started quantum theory, concerns their daily life considerably more. In fact, of the three watershed years for physics toward the beginning of the 20th century-1905: the Special Relativity of Einstein, Lorentz and Poincare; 1915: the General Relativity of Einstein, with its extraordinary reflections on gravitation, space and time; and 1925: the full development of Quantum Mechanics-it is surely the last which has the most profound implications for the development of science and technology. There is no way around it: all physics is quantum, from elementary particles, to stellar physics and the Big Bang, not to mention semiconductors and solar cells."

Contents:

1 Praise of physics 1

1.1 The interplay of the eye and the mind 1

1.2 Advanced technologies 5

1.3 The pillars of contemporary physics 6

1.3.1 Mysteries of light 6

1.3.2 Fundamental structure of matter 8

1.4 The infinitely complex 9

1.5 The Universe 12

2 A quantum phenomenon 13

2.1 Wave behavior of particles 16

2.1.1 Interferences 16

2.1.2 Wave behavior of matter 17

2.1.3 Analysis of the phenomenon 18

2.2 Probabilistic nature of quantum phenomena 20

2.2.1 Random behavior of particles 20

2.2.2 A nonclassical probabilistic phenomenon 20

2.4 Phenomenological description 23

3 Wave function, Schrodinger equation 25

3.1 Terminology and methodology 25

3.1.2 Methodology 26

3.2 Principles of wave mechanics 27

3.2.1 The interference experiment 27

3.2.2 Wave function 27

3.2.3 Schrodinger equation 29

3.3 Superposition principle 30

3.4 Wave packets 31

3.4.1 Free wave packets 31

3.4.2 Fourier transformation 32

3.4.3 Shape of wave packets 33

3.5 Historical landmarks 33

3.6 Momentum probability law 35

3.6.1 Free particle 35

3.6.2 General case 36

3.7 Heisenberg uncertainty relations 36

3.7.1 Size and energy of a quantum system 37

3.7.2 Stability of matter 38

3.8 Controversies and paradoxes 40

3.8.1 The 1927 Solvay Congress 40

3.8.2 The EPR paradox 41

3.8.3 Hidden variables, Bell's inequalities 41

3.8.4 The experimental test 42

4 Physical quantities 45

4.1 Statement of the problem 46

4.1.1 Physical quantities 46

4.1.2 Position and momentum 47

4.2 Observables 48

4.2.1 Position observable 49

4.2.2 Momentum observable 49

4.2.3 Correspondence principle 50

4.2.4 Historical landmarks 50

4.3 A counterexample of Einstein and its consequences 51

4.3.1 What do we know after a measurement? 53

4.3.2 Eigenstates and eigenvalues of an observable 54

4.3.3 Wave packet reduction 55

4.4 The specific role of energy 56

4.4.1 The Hamiltonian 56

4.4.2 The Schrodinger equation, time and energy 57

4.4.3 Stationary states 58

4.4.4 Motion: Interference of stationary states 59

4.5 Schrodinger's cat 60

4.5.1 The dreadful idea 60

4.5.2 The classical world 63

5 Energy quantization 65

5.1 Methodology 65

5.1.1 Bound states and scattering states 66

5.1.2 One-dimensional problems 67

5.2 The harmonic oscillator 67

5.2.1 Harmonic potential 67

5.2.2 Energy levels, eigenfunctions 68

5.3 Square well potentials 69

5.3.1 Square potentials 69

5.3.2 Symmetric square well 70

5.3.3 Infinite well, particle in a box 73

5.4 Double well, the ammonia molecule 74

5.4.1 The model 74

5.4.2 Stationary states, the tunnel effect 75

5.4.3 Energy levels 76

5.4.4 Wave functions 78

5.4.5 Inversion of the molecule 79

5.5 Illustrations and applications of the tunnel effect 81

5.5.1 Sensitivity to the parameters 81

5.5.2 Molecular structure 82

5.6 Tunneling microscopy, nanotechnologies 84

5.6.1 Nanotechnologies 84

5.6.2 Classical limit 85

6 Principles of quantum mechanics 87

6.1 Hilbert space 88

6.1.1 Two-dimensional space 89

6.1.2 Square integrable functions 89

6.2 Dirac formalism 92

6.2.1 Notations 92

6.2.2 Operators 93

6.2.3 Syntax rules 95

6.2.4 Projectors; decomposition of the identity 95

6.3 Measurement results 96

6.3.1 Eigenvectors and eigenvalues of an observable 96

6.3.2 Results of the measurement of a physical quantity 97

6.3.3 Probabilities 98

6.3.4 The Riesz spectral theorem 98

6.3.5 Physical meaning of various representations 100

6.4 Principles of quantum mechanics 101

6.4.1 The principles 101

6.4.2 The case of a continuous spectrum 102

6.4.3 Interest of this synthetic formulation 102

6.5 Heisenberg's matrices 103

6.5.1 Matrix representation of operators 103

6.5.2 Matrices X and P 104

6.5.3 Heisenberg's thoughts 104

6.6 The polarization of light, quantum "logic" 107

7 Two-state systems 113

7.1 The NH[subscript 3] molecule 113

7.2 "Two-state" system 114

7.3 Matrix quantum mechanics 116

7.3.1 Vectors 116

7.3.2 Hamiltonian 117

7.3.3 Observables 117

7.3.5 Basis of classical configurations 119

7.3.6 Interference and measurement 120

7.4 NH[subscript 3] in an electric field 120

7.4.1 Uniform constant field 121

7.4.2 Weak and strong field regimes 122

7.4.3 Other two-state systems 123

7.5 The ammonia molecule in an inhomogeneous field 123

7.5.1 Force on the molecule in an inhomogeneous field 124

7.5.2 Population inversion 126

7.6 Reaction to an oscillating field, the maser 126

7.7 Principle and applications of the maser 128

7.7.1 Amplifiers 129

7.7.2 Oscillators 130

7.7.3 Atomic clocks 130

7.7.4 Tests of relativity 132

7.8 Neutrino oscillations 134

7.8.1 Lepton families 134

7.8.2 Mechanism of the oscillations; reactor neutrinos 135

7.8.3 Successive hermaphroditism of neutrinos 138

8 Algebra of observables 143

8.1 Commutation of observables 143

8.1.1 Fundamental commutation relation 143

8.1.2 Other commutation relations 144

8.1.3 Dirac in the summer of 1925 145

8.2 Uncertainty relations 146

8.3 Evolution of physical quantities 147

8.3.1 Evolution of an expectation value 147

8.3.2 Particle in a potential, classical limit 148

8.3.3 Conservation laws 149

8.4 Algebraic resolution of the harmonic oscillator 150

8.4.1 Operators a, a, and N 151

8.4.2 Determination of the eigenvalues 151

8.4.3 Eigenstates 152

8.5 Commuting observables 154

8.5.1 Theorem 154

8.5.3 Tensor structure of quantum mechanics 155

8.5.4 Complete set of commuting observables (CSCO) 156

8.5.5 Completely prepared quantum state 157

8.6 Sunday, September 20, 1925 158

9 Angular momentum 161

9.1 Fundamental commutation relation 162

9.1.1 Classical angular momentum 162

9.1.2 Definition of an angular momentum observable 162

9.1.3 Results of the quantization 163

9.2 Proof of the quantization 163

9.2.1 Statement of the problem 163

9.2.2 Vectors |j, m > and eigenvalues j and m 164

9.2.3 Operators J[Characters not reproducible] = J[subscript x Characters not reproducible] iJ[subscript y] 165

9.2.4 Quantization 166

9.3 Orbital angular momenta 168

9.3.1 Formulae in spherical coordinates 168

9.3.2 Integer values of m and l 168

9.3.3 Spherical harmonics 169

9.4 Rotation energy of a diatomic molecule 170

9.4.1 Diatomic molecule 171

9.4.2 The CO molecule 172

9.5 Angular momentum and magnetic moment 173

9.5.1 Classical model 173

9.5.2 Quantum transposition 175

9.5.3 Experimental consequences 175

9.5.4 Larmor precession 176

9.5.5 What about half-integer values of j and m? 177

10 The Hydrogen Atom 179

10.1 Two-body problem; relative motion 180

10.2 Motion in a central potential 182

10.2.1 Spherical coordinates, CSCO 182

10.2.2 Eigenfunctions common to H, L[superscript 2], and L[subscript z] 182

10.2.3 Quantum numbers 183

10.3 The hydrogen atom 186

10.3.1 Atomic units; fine structure constant 186

10.3.2 The dimensionless radial equation 188

10.3.3 Spectrum of hydrogen 191

10.3.4 Stationary states of the hydrogen atom 191

10.3.5 Dimensions and orders of magnitude 193

10.3.6 Historical landmarks 194

10.4 Muonic atoms 195

11 Spin 1/2 199

11.1 Experimental results 199

11.2 Spin 1/2 formalism 200

11.2.1 Representation in a particular basis 201

11.2.2 Matrix representation 201

11.3 Complete description of a spin 1/2 particle 202

11.3.1 Observables 203

11.4 Physical spin effects 204

11.5 Spin magnetic moment 205

11.5.1 Hamiltonian of a one-electron atom 205

11.6 The Stern-Gerlach experiment 206

11.6.1 Principle of the experiment 206

11.6.2 Semi-classical analysis 207

11.6.3 Experimental results 208

11.6.4 Explanation of the Stern-Gerlach experiment 208

11.6.5 Successive Stern-Gerlach setups 211

11.6.6 Measurement along an arbitrary axis 211

11.7 The discovery of spin 213

11.7.1 The hidden sides of the Stern-Gerlach experiment 213

11.7.2 Einstein and Ehrenfest's objections 215

11.7.3 Anomalous Zeeman effect 216

11.7.4 Bohr's challenge to Pauli 217

11.7.5 The spin hypothesis 217

11.7.6 The fine structure of atomic lines 218

11.8 Magnetism, magnetic resonance 219

11.8.1 Spin effects, Larmor precession 220

11.8.2 Larmor precession in a fixed magnetic field 221

11.8.3 Rabi's calculation and experiment 221

11.8.4 Nuclear magnetic resonance 225

11.8.5 Magnetic moments of elementary particles 227

11.9 Entertainment: Rotation by 2[pi] of a spin 1/2 228

12 The Pauli Principle 229

12.1 Indistinguishability of two identical particles 230

12.1.1 Identical particles in classical physics 230

12.1.2 The quantum problem 230

12.1.3 Example of ambiguities 231

12.2 Systems of two spin 1/2 particles, total spin 232

12.2.1 The Hilbert space of the problem 232

12.2.2 Hilbert space of spin variables 232

12.2.3 Matrix representation 233

12.2.4 Total spin states 233

12.3 Two-particle system; the exchange operator 235

12.3.1 The Hilbert space for the two-particle system 235

12.3.2 The exchange operator between identical particles 236

12.3.3 Symmetry of the states 237

12.4 The Pauli principle 238

12.4.1 The case of two particles 238

12.4.2 Independent fermions and exclusion principle 239

12.4.3 The case of N identical particles 239

12.5 Physical consequences of the Pauli principle 241

12.5.1 Exchange force between two fermions 241

12.5.2 The ground state of N identical independent particles 241

12.5.3 Behavior of fermion and boson systems at low temperatures 243

13 Entangled states: The way of paradoxes 247

13.1 The EPR paradox 247

13.2 The version of David Bohm 249

13.2.1 Bell's inequality 251

13.2.2 Experimental tests 254

13.3 Quantum cryptography; how to enjoy a nuisance 256

13.3.1 The communication between Alice and Bob 256

13.3.2 Present experimental setups 258

13.4 Quantum teleportation 260

13.4.1 Bell states 260

13.4.2 Teleportation 261

14 Quantum mechanics in the Universe 263

14.1 Quantum mechanics and astronomy 265

14.1.1 Life and death of stars 265

14.1.2 Spectroscopy 268

14.2 Radioastronomy, the interstellar medium 268

14.2.1 The interstellar medium 269

14.3 Cosmic background radiation: Birth of the Universe 273

14.4 The 21-cm line of hydrogen 275

14.4.1 Hyperfine structure of hydrogen 276

14.4.2 Hydrogen maser 278

14.4.3 Importance of the 21-cm line 279

14.5 The Milky Way 280

14.6 The intergalactic medium; star wars 281

14.6.1 Spiral arms, birthplaces of stars 285

14.7 Interstellar molecules, the origin of life 287

14.7.1 Rotation spectra of molecules 287

14.7.2 Interstellar molecules 288

14.7.3 The origin of life 289

14.8 Where are they? Quantum mechanics, the universal cosmic language 291

14.8.1 Life, intelligence, and thought 291

14.8.2 Listening to extraterrestrials 293

14.8.3 Quantum mechanics, the universal cosmic language 295.

Notes:

Includes bibliographical references and index.

ISBN:

0387377425

9780387377421

0387377441

9780387377445

OCLC:

123410782