Lectures on Quantum Mechanics

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 = mc2'. 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 Poincaré; 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." A graduate of the Ecole Normale Superieure, Jean-Louis Basdevant is Professor and former Chair of the Department of Physics at the Ecole Polytechnique, and Director of Research for the CNRS. Specializing in the theoretical physics of elementary particles, quantum field theory and astrophysics, Prof. Basdevant works in the Leprince-Ringuet Laboratory at the Ecole Polytechnique. Cover Page......Page 1 Litle Page......Page 3 ISBN 0387377425......Page 4 3 Wave function, Schrödinger equation......Page 6 5 Energy quantization......Page 7 6 Principles of quantum mechanics......Page 8 8 Algebra of observables......Page 9 10 The Hydrogen Atom......Page 10 12 The Pauli Principle......Page 11 14 Quantum mechanics in the Universe......Page 12 Index......Page 13 Preface......Page 14 1.1 The interplay of the eye and the mind......Page 16 1.2 Advanced technologies......Page 20 1.3.1 Mysteries of light......Page 21 1.3.2 Fundamental structure of matter......Page 23 1.4 The infinitely complex......Page 24 Materials......Page 25 1.5 The Universe......Page 27 2 A quantum phenomenon......Page 28 2.1.1 Interferences......Page 31 2.1.2 Wave behavior of matter......Page 32 2.1.3 Analysis of the phenomenon......Page 33 2.2.2 A nonclassical probabilistic phenomenon......Page 35 2.3 Conclusions......Page 36 2.4 Phenomenological description......Page 38 3.1.1 Terminology......Page 40 3.1.2 Methodology......Page 41 3.2.2 Wave function......Page 42 3.2.3 Schr ̈odinger equation......Page 44 3.3 Superposition principle......Page 45 3.4.1 Free wave packets......Page 46 3.4.2 Fourier transformation......Page 47 3.5 Historical landmarks......Page 48 3.6.1 Free particle......Page 50 3.7 Heisenberg uncertainty relations......Page 51 3.7.1 Size and energy of a quantum system......Page 52 3.7.2 Stability of matter......Page 53 3.8.1 The 1927 Solvay Congress......Page 55 3.8.3 Hidden variables, Bell’s inequalities......Page 56 3.8.4 The experimental test......Page 57 4 Physical quantities......Page 60 4.1.1 Physical quantities......Page 61 4.1.2 Position and momentum......Page 62 4.2 Observables......Page 63 4.2.2 Momentum observable......Page 64 4.2.4 Historical landmarks......Page 65 4.3 A counterexample of Einstein and its consequences......Page 66 4.3.1 What do we know after a measurement?......Page 68 4.3.2 Eigenstates and eigenvalues of an observable......Page 69 4.3.3 Wave packet reduction......Page 70 4.4.1 The Hamiltonian......Page 71 4.4.2 The Schrödinger equation, time and energy......Page 72 4.4.3 Stationary states......Page 73 4.4.4 Motion: Interference of stationary states......Page 74 4.5.1 The dreadful idea......Page 75 4.5.2 The classical world......Page 78 5.1 Methodology......Page 80 5.1.1 Bound states and scattering states......Page 81 Eigenvalues, eigenfunctions......Page 82 5.2.2 Energy levels, eigenfunctions......Page 83 5.3.1 Square potentials......Page 84 5.3.2 Symmetric square well......Page 85 5.3.3 Infinite well, particle in a box......Page 88 5.4.1 The model......Page 89 5.4.2 Stationary states, the tunnel effect......Page 90 5.4.3 Energy levels......Page 91 5.4.4 Wave functions......Page 93 5.4.5 Inversion of the molecule......Page 94 5.5.1 Sensitivity to the parameters......Page 96 Valence electrons......Page 97 Potential barriers......Page 98 5.6.1 Nanotechnologies......Page 99 5.6.2 Classical limit......Page 100 6 Principles of quantum mechanics......Page 102 6.1 Hilbert space......Page 103 6.1.2 Square integrable functions......Page 104 Vectors......Page 107 6.2.2 Operators......Page 108 6.2.4 Projectors; decomposition of the identity......Page 110 6.3.1 Eigenvectors and eigenvalues of an observable......Page 111 6.3.2 Results of the measurement of a physical quantity......Page 112 6.3.4 The Riesz spectral theorem......Page 113 6.3.5 Physical meaning of various representations......Page 115 6.4.1 The principles......Page 116 6.4.3 Interest of this synthetic formulation......Page 117 6.5.1 Matrix representation of operators......Page 118 6.5.3 Heisenberg’s thoughts......Page 119 6.6 The polarization of light, quantum “logic”......Page 122 Quantum “logic”......Page 125 7.1 The NH3 molecule......Page 128 7.2 “Two-state” system......Page 129 7.3.1 Vectors......Page 131 7.3.3 Observables......Page 132 Position observable......Page 133 7.3.5 Basis of classical configurations......Page 134 7.4 NH3 in an electric field......Page 135 7.4.1 Uniform constant field......Page 136 Weak field......Page 137 7.5 The ammonia molecule in an inhomogeneous field......Page 138 7.5.1 Force on the molecule in an inhomogeneous field......Page 139 7.6 Reaction to an oscillating field, the maser......Page 141 7.7 Principle and applications of the maser......Page 143 7.7.1 Amplifiers......Page 144 7.7.3 Atomic clocks......Page 145 7.7.4 Tests of relativity......Page 147 7.8.1 Lepton families......Page 149 7.8.2 Mechanism of the oscillations; reactor neutrinos......Page 150 Results......Page 152 7.8.3 Successive hermaphroditism of neutrinos......Page 153 8.1.1 Fundamental commutation relation......Page 158 8.1.2 Other commutation relations......Page 159 8.1.3 Dirac in the summer of 1925......Page 160 8.2 Uncertainty relations......Page 161 8.3.1 Evolution of an expectation value......Page 162 8.3.2 Particle in a potential, classical limit......Page 163 8.3.3 Conservation laws......Page 164 8.4 Algebraic resolution of the harmonic oscillator......Page 165 8.4.2 Determination of the eigenvalues......Page 166 Ground state......Page 167 Excited states......Page 168 8.5.1 Theorem......Page 169 8.5.3 Tensor structure of quantum mechanics......Page 170 8.5.4 Complete set of commuting observables (CSCO)......Page 171 8.5.5 Completely prepared quantum state......Page 172 8.6 Sunday, September 20, 1925......Page 173 9 Angular momentum......Page 176 9.1.2 Definition of an angular momentum observable......Page 177 9.2.1 Statement of the problem......Page 178 9.2.2 Vectors |j,m> and eigenvalues j and m......Page 179 9.2.3 Operators Ĵ± =Ĵx ± iĴy......Page 180 9.2.4 Quantization......Page 181 Construction of the states |j,m>......Page 182 9.3.2 Integer values of m and l......Page 183 Examples of spherical harmonics......Page 184 9.4 Rotation energy of a diatomic molecule......Page 185 9.4.1 Diatomic molecule......Page 186 9.4.2 The CO molecule......Page 187 9.5.1 Classical model......Page 188 Orbital angular momenta......Page 190 9.5.4 Larmor precession......Page 191 9.5.5 What about half-integer values of j and m?......Page 192 10 The Hydrogen Atom......Page 194 10.1 Two-body problem; relative motion......Page 195 Separation of the angular variables......Page 197 10.2.3 Quantum numbers......Page 198 The principal quantum number n......Page 199 Spectroscopic notation (states s, p, d, f, ...)......Page 200 10.3.1 Atomic units; fine structure constant......Page 201 Fine structure constant......Page 202 10.3.2 The dimensionless radial equation......Page 203 At infinity......Page 205 The ground state (1s)......Page 206 Other states......Page 207 10.3.5 Dimensions and orders of magnitude......Page 208 Spectroscopy......Page 209 10.4 Muonic atoms......Page 210 11.1 Experimental results......Page 214 11.2 Spin 1/2 formalism......Page 215 11.2.2 Matrix representation......Page 216 11.3 Complete description of a spin 1/2 particle......Page 217 11.3.1 Observables......Page 218 11.4 Physical spin effects......Page 219 11.5.1 Hamiltonian of a one-electron atom......Page 220 11.6.1 Principle of the experiment......Page 221 11.6.2 Semi-classical analysis......Page 222 11.6.4 Explanation of the Stern–Gerlach experiment......Page 223 11.6.6 Measurement along an arbitrary axis......Page 226 11.7.1 The hidden sides of the Stern–Gerlach experiment......Page 228 11.7.2 Einstein and Ehrenfest’s objections......Page 230 11.7.3 Anomalous Zeeman effect......Page 231 11.7.5 The spin hypothesis......Page 232 11.7.6 The fine structure of atomic lines......Page 233 11.8 Magnetism, magnetic resonance......Page 234 Uncorrelated space and spin variables......Page 235 Superposition of a fixed field and a rotating field......Page 236 Rabi’s experiment......Page 238 11.8.4 Nuclear magnetic resonance......Page 240 11.8.5 Magnetic moments of elementary particles......Page 242 11.9 Entertainment: Rotation by 2π of a spin 1/2......Page 243 12 The Pauli Principle......Page 244 12.1.2 The quantum problem......Page 245 12.1.3 Example of ambiguities......Page 246 12.2.2 Hilbert space of spin variables......Page 247 12.2.4 Total spin states......Page 248 12.3.1 The Hilbert space for the two-particle system......Page 250 Examples......Page 251 12.3.3 Symmetry of the states......Page 252 Examples......Page 253 12.4.3 The case of N identical particles......Page 254 The case of fermions......Page 255 12.5.2 The ground state of N identical independent particles......Page 256 12.5.3 Behavior of fermion and boson systems at identical independent particles......Page 258 13.1 The EPR paradox......Page 262 13.2 The version of David Bohm......Page 264 13.2.1 Bell’s inequality......Page 266 13.2.2 Experimental tests......Page 269 13.3.1 The communication between Alice and Bob......Page 271 13.3.2 Present experimental setups......Page 273 13.4.1 Bell states......Page 275 13.4.2 Teleportation......Page 276 Further reading......Page 277 14 Quantum mechanics in the Universe......Page 278 14.1.1 Life and death of stars......Page 280 14.2 Radioastronomy, the interstellar medium......Page 283 14.2.1 The interstellar medium......Page 284 14.3 Cosmic background radiation: Birth of the Universe......Page 288 14.4 The 21-cm line of hydrogen......Page 290 14.4.1 Hyperfine structure of hydrogen......Page 291 14.4.2 Hydrogen maser......Page 293 14.4.3 Importance of the 21-cm line......Page 294 14.5 The Milky Way......Page 295 14.6 The intergalactic medium; star wars......Page 296 14.6.1 Spiral arms, birthplaces of stars......Page 300 14.7.1 Rotation spectra of molecules......Page 302 14.7.2 Interstellar molecules......Page 303 14.7.3 The origin of life......Page 304 14.8.1 Life, intelligence, and thought......Page 306 14.8.2 Listening to extraterrestrials......Page 308 14.8.3 Quantum mechanics, the universal cosmic language......Page 310 Index......Page 318 Beautifully illustrated and engagingly written, Twelve Lectures in 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 = mc2’. In fact, of the three watershed years for physics toward the beginning of the 20th century – 1905: the Special Relativity of Einstein, Lorentz and Poincaré; 1915: the General Relativity of Einstein, with its extraordinary reflections on gravitation, space and time; and 1925: the 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." A graduate of the Ecole Normale Superieure, Jean-Louis Basdevant is Professor and Chair of the Department of Physics at the Ecole Polytechnique, and Director of Research for the CNRS. Specializing in the theoretical physics of elementary particles, quantum field theory and astrophysics, Prof. Basdevant works in the Leprince-Ringuet Laboratory at the Ecole Polytechnique. Beautifully illustrated and engagingly written, Twelve Lectures in 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 lecture that can be followed 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 = mc2’.... 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." 1. Praise Of Physics -- 2. A Quantum Phenomenon -- 3. Wave Function, Schrodinger Equation -- 4. Physical Quantities -- 5. Energy Quantization -- 6. Principles Of Quantum Mechanics -- 7. Two-state Systems -- 8. Algebra Of Observables -- 9. Angular Momentum -- 10. The Hydrogen Atom -- 11. Spin 1/2 -- 12. The Pauli Principle -- 13. Entangled States : The Way Of Paradoxes -- 14. Quantum Mechanics In The Universe. Jean-louis Basdevant. Includes Bibliographical References And Index.