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Quantum mechanics: with 92 exercises with solutions

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Bibliographische Detailangaben
Beteiligte Personen:	Basdevant, Jean-Louis 1939- (VerfasserIn), Dalibard, Jean 1958- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 2005
Ausgabe:	Corr. 2. print.
Schlagwörter:	Quantenmechanik Lehrbuch
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015693108&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XXII, 511 S. Ill., graph. Darst. 1 CD-Rom (12 cm)
ISBN:	3540277064 9783540277064

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Datensatz im Suchindex

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adam_text	Contents Physical Constants ......................................... XXIII 1. Quantum Phenomena ..................................... 1 1.1 The Franck and Hertz Experiment ........................ 3 1.2 Interference of Matter Waves ............................. 5 1.2.1 The Young Double-Slit Experiment ................. 6 1.2.2 Interference of Atoms in a Double-Slit Experiment .... 7 1.2.3 Probabilistic Aspect of Quantum Interference ........ 8 1.3 The Experiment of Davisson and Germer .................. 10 1.3.1 Diffraction of X Rays by a Crystal .................. 10 1.3.2 Electron Diffraction .............................. 12 1.4 Summary of a Few Important Ideas ....................... 15 Further Reading ............................................ 15 Exercises .................................................. 16 2. The Wave Function and the Schrödinger Equation ........ 17 2.1 The Wave Function ..................................... 18 2.1.1 Description of the State of a Particle ................ 18 2.1.2 Position Measurement of the Particle ............... 19 2.2 Interference and the Superposition Principle ............... 20 2.2.1 De Broglie Waves ................................ 20 2.2.2 The Superposition Principle ....................... 21 2.2.3 The Wave Equation in Vacuum .................... 22 2.3 Free Wave Packets ...................................... 24 2.3.1 Definition of a Wave Packet ....................... 24 2.3.2 Fourier Transformation ............................ 24 2.3.3 Structure of the Wave Packet ...................... 25 2.3.4 Propagation of a Wave Packet: the Group Velocity ... 26 2.3.5 Propagation of a Wave Packet: Average Position and Spreading .................... 27 2.4 Momentum Measurements and Uncertainty Relations ....... 28 2.4.1 The Momentum Probability Distribution ............ 29 2.4.2 Heisenberg Uncertainty Relations ................... 30 2.5 The Schrödinger Equation ............................... 31 XII Contents 2.5.1 Equation of Motion ............................... 32 2.5.2 Particle in a Potential: Uncertainty Relations ........ 32 2.5.3 Stability of Matter ............................... 33 2.6 Momentum Measurement in a Time-of-Flight Experiment ... 34 Further Reading ............................................ 36 Exercises .................................................. 37 3. Physical Quantities and Measurements ................... 39 3.1 Measurements in Quantum Mechanics ..................... 40 3.1.1 The Measurement Procedure ....................... 40 3.1.2 Experimental Facts ............................... 41 3.1.3 Reinterpretation of Position and Momentum Measurements ..................... 41 3.2 Physical Quantities and Observables ...................... 42 3.2.1 Expectation Value of a Physical Quantity ........... 42 3.2.2 Position and Momentum Observables ............... 43 3.2.3 Other Observables: the Correspondence Principle ..... 44 3.2.4 Commutation of Observables ...................... 44 3.3 Possible Results of a Measurement ........................ 45 3.3.1 Eigenfunctions and Eigenvalues of an Observable ..... 45 3.3.2 Results of a Measurement and Reduction of the Wave Packet .................. 46 3.3.3 Individual Versus Multiple Measurements ........... 47 3.3.4 Relation to Heisenberg Uncertainty Relations ........ 47 3.3.5 Measurement and Coherence of Quantum Mechanics .. 48 3.4 Energy Eigenfunctions and Stationary States ............... 48 3.4.1 Isolated Systems: Stationary States ................. 49 3.4.2 Energy Eigenstates and Time Evolution ............. 50 3.5 The Probability Current ................................. 50 3.6 Crossing Potential Barriers .............................. 52 3.6.1 The Eigenstates of the Hamiltonian ................. 52 3.6.2 Boundary Conditions at the Discontinuities of the Potential .................................. 53 3.6.3 Reflection and Transmission on a Potential Step ...... 54 3.6.4 Potential Barrier and Tunnel Effect ................. 56 3.7 Summary of Chapters 2 and 3............................ 57 Further Reading ............................................ 59 Exercises .................................................. 60 4. Quantization of Energy in Simple Systems ................ 63 4.1 Bound States and Scattering States ....................... 63 4.1.1 Stationary States of the Schrödinger Equation ....... 64 4.1.2 Bound States .................................... 64 4.1.3 Scattering States ................................. 65 4.2 The One Dimensional Harmonic Oscillator ................. 66 Contents XIII 4.2.1 Definition and Classical Motion .................... 66 4.2.2 The Quantum Harmonic Oscillator ................. 67 4.2.3 Examples ....................................... 69 4.3 Square-Well Potentials .................................. 70 4.3.1 Relevance of Square Potentials ..................... 70 4.3.2 Bound States in a One-Dimensional Square-Well Potential ............................. 71 4.3.3 Infinite Square Well .............................. 73 4.3.4 Particle in a Three-Dimensional Box ................ 74 4.4 Periodic Boundary Conditions ........................... 75 4.4.1 A One-Dimensional Example ...................... 75 4.4.2 Extension to Three Dimensions .................... 77 4.4.3 Introduction of Phase Space ....................... 78 4.5 The Double Well Problem and the Ammonia Molecule ...... 78 4.5.1 Model of the NH3 Molecule ........................ 79 4.5.2 Wave Functions .................................. 79 4.5.3 Energy Levels .................................... 81 4.5.4 The Tunnel Effect and the Inversion Phenomenon .... 82 4.6 Other Applications of the Double Well .................... 84 Further Reading ............................................ 86 Exercises .................................................. 87 5. Principles of Quantum Mechanics ......................... 89 5.1 Hilbert Space .......................................... 90 5.1.1 The State Vector ................................. 90 5.1.2 Scalar Products and the Dirac Notations ............ 90 5.1.3 Examples ....................................... 91 5.1.4 Bras and Kets, Brackets ........................... 92 5.2 Operators in Hilbert Space .............................. 92 5.2.1 Matrix Elements of an Operator .................... 92 5.2.2 Adjoint Operators and Hermitian Operators ......... 93 5.2.3 Eigenvectors and Eigenvalues ...................... 94 5.2.4 Summary: Syntax Rules in Dirac s Formalism ........ 95 5.3 The Spectral Theorem .................................. 95 5.3.1 ffilbertian Bases ................................. 95 5.3.2 Projectors and Closure Relation .................... 96 5.3.3 The Spectral Decomposition of an Operator ......... 96 5.3.4 Matrix Representations ........................... 97 5.4 Measurement of Physical Quantities ...................... 99 5.5 The Principles of Quantum Mechanics ....................100 5.6 Structure of Hilbert Space ...............................104 5.6.1 Tensor Products of Spaces .........................104 5.6.2 The Appropriate Hilbert Space .....................105 5.6.3 Properties of Tensor Products ......................105 5.6.4 Operators in a Tensor Product Space ...............106 XIV Contents 5.6.5 Simple Examples .................................106 5.7 Reversible Evolution and the Measurement Process .........107 Further Reading ............................................110 Exercises .................................................. Ill 6. Two-State Systems, Principle of the Maser...............115 6.1 Two-Dimensional Hubert Space ..........................115 6.2 A Familiar Example: the Polarization of Light .............116 6.2.1 Polarization States of a Photon .................... 116 6.2.2 Measurement of Photon Polarizations ............... 118 6.2.3 Successive Measurements and Quantum Logic ...... 119 6.3 The Model of the Ammonia Molecule ..................... 120 6.3.1 Restriction to a Two-Dimensional Hubert Space ......120 6.3.2 The Basis { фѕ), Џа)} ............................ 121 6.3.3 The Basis {\|^r>, \|^l» ............................ 123 6.4 The Ammonia Molecule in an Electric Field ...............123 6.4.1 The Coupling of NH3 to an Electric Field ...........124 6.4.2 Energy Levels in a Fixed Electric Field ..............125 6.4.3 Force Exerted on the Molecule by an Inhomogeneous Field ........................127 6.5 Oscillating Fields and Stimulated Emission ................129 6.6 Principle and Applications of Masers......................131 6.6.1 Amplifier ........................................131 6.6.2 Oscillator .......................................132 6.6.3 Atomic Clocks ...................................132 Further Reading ............................................132 Exercises ..................................................133 7. Commutation of Observables .............................135 7.1 Commutation Relations .................................136 7.2 Uncertainty Relations ...................................137 7.3 Ehrenfest s Theorem ....................................138 7.3.1 Evolution of the Expectation Value of an Observable. . 138 7.3.2 Particle in a Potential V{r) ........................139 7.3.3 Constants of Motion ..............................140 7.4 Commuting Observables .................................142 7.4.1 Existence of a Common Eigenbasis for Commuting Observables .......................142 7.4.2 Complete Set of Commuting Observables (CSCO) ___142 7.4.3 Completely Prepared Quantum State ...............143 7.4.4 Symmetries of the Hamiltonian and Search of Its Eigenstates ......................145 7.5 Algebraic Solution of the Harmonic-Oscillator Problem ......148 7.5.1 Reduced Variables ................................148 7.5.2 Annihilation and Creation Operators α and ał .......148 Contents XV 7.5.3 Eigenvalues of the Number Operator Ń .............149 7.5.4 Eigenstates ......................................150 Further Reading ............................................151 Exercises ..................................................152 8. The Stern-Gerlach Experiment ...........................157 8.1 Principle of the Experiment ..............................157 8.1.1 Classical Analysis ................................157 8.1.2 Experimental Results .............................159 8.2 The Quantum Description of the Problem .................161 8.3 The Observables ßx and μυ.............................. 163 8.4 Discussion .............................................165 8.4.1 Incompatibility of Measurements Along Different Axes 165 8.4.2 Classical Versus Quantum Analysis ................. 166 8.4.3 Measurement Along an Arbitrary Axis .............. 167 8.5 Complete Description of the Atom ........................ 168 8.5.1 Hubert Space ....................................168 8.5.2 Representation of States and Observables ............169 8.5.3 Energy of the Atom in a Magnetic Field .............170 8.6 Evolution of the Atom in a Magnetic Field ................170 8.6.1 Schrödinger Equation .............................170 8.6.2 Evolution in a Uniform Magnetic Field ..............171 8.6.3 Explanation of the Stern-Gerlach Experiment ........173 8.7 Conclusion ............................................175 Further Reading ............................................175 Exercises ..................................................176 9. Approximation Methods ..................................177 9.1 Perturbation Theory ....................................177 9.1.1 Definition of the Problem ..........................177 9.1.2 Power Expansion of Energies and Eigenstates ........178 9.1.3 First-Order Perturbation in the Nondegenerate Case .. 179 9.1.4 First-Order Perturbation in the Degenerate Case .....179 9.1.5 First-Order Perturbation to the Eigenstates ..........180 9.1.6 Second-Order Perturbation to the Energy Levels .....181 9.1.7 Examples .......................................181 9.1.8 Remarks on the Convergence of Perturbation Theory . 182 9.2 The Variational Method .................................183 9.2.1 The Ground State ................................183 9.2.2 Other Levels .....................................184 9.2.3 Examples of Applications of the Variational Method .. 185 Exercises ..................................................187 XVI Contents 10. Angular Momentum ......................................189 10.1 Orbital Angular Momentum and the Commutation Relations 190 10.2 Eigenvalues of Angular Momentum .......................190 10.2.1 The Observables J2 and Jz and the Basis States j, m) 191 10.2.2 The Operators J± ................................192 10.2.3 Action of J± on the States j,m) ...................192 10.2.4 Quantization of j and m ..........................193 10.2.5 Measurement of Jx and Jy .........................195 10.3 Orbital Angular Momentum .............................196 10.3.1 The Quantum Numbers m and і are Integers ........196 10.3.2 Spherical Coordinates .............................197 10.3.3 Eigenfunctions of L2 and Lz: the Spherical Harmonics 198 10.3.4 Examples of Spherical Harmonics ...................199 10.3.5 Example: Rotational Energy of a Diatomic Molecule .. 200 10.4 Angular Momentum and Magnetic Moment ................201 10.4.1 Orbital Angular Momentum and Magnetic Moment ... 202 10.4.2 Generalization to Other Angular Momenta ..........203 10.4.3 What Should we Think about Half-Integer Values of j and m ?..............204 Further Reading ............................................204 Exercises ..................................................205 11. Initial Description of Atoms ..............................207 11.1 The Two-Body Problem; Relative Motion .................208 11.2 Motion in a Central Potential ............................210 11.2.1 Spherical Coordinates .............................210 11.2.2 Eigenfunctions Common to ff , Ì? and Lz ...........211 11.3 The Hydrogen Atom ....................................215 11.3.1 Orders of Magnitude: Appropriate Units in Atomic Physics ...............215 11.3.2 The Dimensionless Radial Equation .................216 11.3.3 Spectrum of Hydrogen ............................219 11.3.4 Stationary States of the Hydrogen Atom ............220 11.3.5 Dimensions and Orders of Magnitude ...............221 11.3.6 Time Evolution of States of Low Energies ...........223 11.4 Hydrogen-Like Atoms ...................................224 11.5 Muonic Atoms .........................................224 11.6 Spectra of Alkali Atoms .................................226 Further Reading ............................................227 Exercises ..................................................228 Contents XVII 12. Spin 1/2 and Magnetic Resonance ........................231 12.1 The Hubert Space of Spin 1/2 ...........................232 12.1.1 Spin Observables .................................233 12.1.2 Representation in a Particular Basis ................233 12.1.3 Matrix Representation ............................234 12.1.4 Arbitrary Spin State ..............................234 12.2 Complete Description of a Spin-1/2 Particle ...............235 12.2.1 Hubert Space ....................................235 12.2.2 Representation of States and Observables ............235 12.3 Spin Magnetic Moment .................................236 12.3.1 The Stern-Gerlach Experiment .....................236 12.3.2 Anomalous Zeeman Effect .........................237 12.3.3 Magnetic Moment of Elementary Particles ...........237 12.4 Uncorrelated Space and Spin Variables ....................238 12.5 Magnetic Resonance ....................................239 12.5.1 Larmor Precession in a Fixed Magnetic Field Bq ..... 239 12.5.2 Superposition of a Fixed Field and a Rotating Field .. 240 12.5.3 Rabi s Experiment ................................ 242 12. Ъ A Applications of Magnetic Resonance ................ 244 12.5.5 Rotation of a Spin 1/2 Particle by 2тг ............... 245 Further Reading ............................................ 246 Exercises .................................................. 247 13. Addition of Angular Momenta, Fine and Hyperfine Structure of Atomic Spectra .........249 13.1 Addition of Angular Momenta ...........................249 13.1.1 The Total-Angular Momentum Operator ............249 13.1.2 Factorized and Coupled Bases ......................250 13.1.3 A Simple Case: the Addition of Two Spins of 1/2.....251 13.1.4 Addition of Two Arbitrary Angular Momenta ........254 13.1.5 One-Electron Atoms, Spectroscopie Notations ........258 13.2 Fine Structure of Monovalent Atoms ......................258 13.3 Hyperfine Structure; the 21 cm Line of Hydrogen ...........261 13.3.1 Interaction Energy ...............................261 13.3.2 Perturbation Theory ..............................262 13.3.3 Diagonalization of Hi .............................263 13.3.4 The Effect of an External Magnetic Field ............265 13.3.5 The 21 cm Line in Astrophysics ....................265 Further Reading ............................................268 Exercises ..................................................269 XVIII Contents 14. Entangled States, EPR Paradox and Bell s Inequality .....273 Written in collaboration with Philippe Grangier 14.1 The EPR Paradox and Bell s Inequality ...................274 14.1.1 God Does not Play Dice .........................274 14.1.2 The EPR Argument ..............................275 14.1.3 Bell s Inequality ..................................278 14.1.4 Experimental Tests ...............................281 14.2 Quantum Cryptography .................................282 14.2.1 The Communication Between Alice and Bob .........282 14.2.2 The Quantum Noncloning Theorem .................285 14.2.3 Present Experimental Setups ......................286 14.3 The Quantum Computer ................................287 14.3.1 The Quantum Bits, or Q-Bits ....................287 14.3.2 The Algorithm of Peter Shor .......................288 14.3.3 Principle of a Quantum Computer ..................289 14.3.4 Decoherence .....................................290 Further Reading ............................................290 Exercises ..................................................291 15. The Lagrangian and Hamiltonian Formalisms, Lorentz Force in Quantum Mechanics .....................293 15.1 Lagrangian Formalism and the Least-Action Principle .......294 15.1.1 Least Action Principle ............................294 15.1.2 Lagrange Equations ..............................295 15.1.3 Energy ..........................................297 15.2 Canonical Formalism of Hamilton ........................297 15.2.1 Conjugate Momenta ..............................297 15.2.2 Canonical Equations ..............................298 15.2.3 Poisson Brackets .................................299 15.3 Analytical Mechanics and Quantum Mechanics .............300 15.4 Classical Charged Particles in an Electromagnetic Field .....301 15.5 Lorentz Force in Quantum Mechanics .....................302 15.5.1 Hamiltonian .....................................302 15.5.2 Gauge Invariance .................................303 15.5.3 The Hydrogen Atom Without Spin in a Uniform Magnetic Field .......................304 15.5.4 Spin-1/2 Particle in an Electromagnetic Field ........305 Further Reading ............................................305 Exercises ..................................................305 16. Identical Particles and the Pauli Principle ................309 16.1 Indistinguishability of Two Identical Particles ..............310 16.1.1 Identical Particles in Classical Physics ..............310 16.1.2 The Quantum Problem ...........................310 16.2 Two-Particle Systems; the Exchange Operator .............312 Contents XIX 16.2.1 The Hilbert Space for the Two Particle System .......312 16.2.2 The Exchange Operator Between Two Identical Particles ....................312 16.2.3 Symmetry of the States ...........................313 16.3 The Pauli Principle .....................................314 16.3.1 The Case of Two Particles ......................... 314 16.3.2 Independent Fermions and Exclusion Principle ....... 315 16.3.3 The Case of N Identical Particles .................. 316 16.3.4 Time Evolution .................................. 317 16.4 Physical Consequences of the Pauli Principle ............... 317 16.4.1 Exchange Force Between Two Fermions .............318 16.4.2 The Ground State of TV Identical Independent Particles ................318 16.4.3 Behavior of Fermion and Boson Systems at Low Temperature ..............................320 16.4.4 Stimulated Emission and the Laser Effect ...........322 16.4.5 Uncertainty Relations for a System of N Fermions .... 323 16.4.6 Complex Atoms and Atomic Shells .................324 Further Reading ............................................326 Exercises ..................................................327 17. The Evolution of Systems .................................331 Written in collaboration with Gilbert Grynberg 17.1 Time-Dependent Perturbation Theory .....................332 17.1.1 Transition Probabilities ...........................332 17.1.2 Evolution Equations ..............................332 17.1.3 Perturbative Solution .............................333 17.1.4 First-Order Solution: the Born Approximation .......334 17.1.5 Particular Cases ..................................334 17.1.6 Perturbative and Exact Solutions ...................335 17.2 Interaction of an Atom with an Electromagnetic Wave ......336 17.2.1 The Electric-Dipole Approximation .................336 17.2.2 Justification of the Electric Dipole Interaction ........337 17.2.3 Absorption of Energy by an Atom ..................338 17.2.4 Selection Rules ...................................339 17.2.5 Spontaneous Emission ............................339 17.2.6 Control of Atomic Motion by Light .................341 17.3 Decay of a System ......................................343 17.3.1 The Radioactivity of 57Fe .........................343 17.3.2 The Fermi Golden Rule ...........................345 17.3.3 Orders of Magnitude ..............................346 17.3.4 Behavior for Long Times ..........................347 17.4 The Time-Energy Uncertainty Relation ...................350 17.4.1 Isolated Systems and Intrinsic Interpretations ........350 17.4.2 Interpretation of Landau and Peierls ................351 XX Contents 17.4.3 The Einstein-Bohr Controversy ....................352 Further Reading ............................................353 Exercises ..................................................353 18. Scattering Processes ......................................357 18.1 Concept of Cross Section ................................358 18.1.1 Definition of Cross Section .........................358 18.1.2 Classical Calculation ..............................359 18.1.3 Examples .......................................360 18.2 Quantum Calculation in the Born Approximation ..........361 18.2.1 Asymptotic States ................................361 18.2.2 Transition Probability ............................362 18.2.3 Scattering Cross Section ...........................363 18.2.4 Validity of the Born Approximation ................364 18.2.5 Example: the Yukawa Potential ....................365 18.2.6 Range of a Potential in Quantum Mechanics .........366 18.3 Exploration of Composite Systems ........................367 18.3.1 Scattering Off a Bound State and the Form Factor ... 367 18.3.2 Scattering by a Charge Distribution ................368 18.4 General Scattering Theory ...............................372 18.4.1 Scattering States ................................. 372 18.4.2 The Scattering Amplitude ......................... 373 18.4.3 The Integral Equation for Scattering ................ 374 18.5 Scattering at Low Energy ............................... 375 18.5.1 The Scattering Length ............................375 18.5.2 Explicit Calculation of a Scattering Length ..........376 18.5.3 The Case of Identical Particles .....................377 Further Reading ............................................378 Exercises ..................................................378 19. Qualitative Physics on a Macroscopic Scale ...............381 Written in collaboration with Alfred Vidal-Madjar 19.1 Confined Particles and Ground State Energy ...............382 19.1.1 The Quantum Pressure ...........................382 19.1.2 Hydrogen Atom ..................................383 19.1.3 iV-Fermion Systems and Complex Atonas ............383 19.1.4 Molecules, Liquids and Solids ......................384 19.1.5 Hardness of a Solid ...............................385 19.2 Gravitational Versus Electrostatic Forces ..................386 19.2.1 Screening of Electrostatic Interactions ...............386 19.2.2 Additivity of Gravitational Interactions .............387 19.2.3 Ground State of a Gravity-Dominated Object ........388 19.2.4 Liquefaction of a Solid and the Height of Mountains .. 390 19.3 White Dwarfs, Neutron Stars and the Gravitational Catastrophe ........................392 Contents XXI 19.3.1 White Dwarfs and the Chandrasekhar Mass .........392 19.3.2 Neutron Stars ....................................394 Further Reading ............................................396 20. Early History of Quantum Mechanics .....................397 20.1 The Origin of Quantum Concepts ........................397 20.1.1 Planck s Radiation Law ...........................397 20.1.2 Photons .........................................398 20.2 The Atomic Spectrum ..................................398 20.2.1 Empirical Regularities of Atomic Spectra ............398 20.2.2 The Structure of Atoms ...........................399 20.2.3 The Bohr Atom ..................................399 20.2.4 The Old Theory of Quanta ........................400 20.3 Spin ..................................................400 20.4 Heisenberg s Matrices ...................................401 20.5 Wave Mechanics ........................................403 20.6 The Mathematical Formalization .........................404 20.7 Some Important Steps in More Recent Years ...............405 Further Reading ............................................406 Appendix A. Concepts of Probability Theory ...............407 1 Fundamental Concepts ..................................407 2 Examples of Probability Laws ............................408 2.1 Discrete Laws ....................................408 2.2 Continuous Probability Laws in One or Several Variables ........................408 3 Random Variables ......................................409 3.1 Definition .......................................409 3.2 Conditional Probabilities ..........................410 3.3 Independent Random Variables ....................411 3.4 Binomial Law and the Gaussian Approximation ......411 4 Moments of Probability Distributions .....................412 4.1 Mean Value or Expectation Value ..................412 4.2 Variance and Mean Square Deviation ...............412 4.3 Bienaymé-Tchebycheff Inequality ...................413 4.4 Experimental Verification of a Probability Law .......413 Exercises ..................................................414 Appendix B. Dirac Distribution, Fourier Transformation .... 417 1 Dirac Distribution, or б Function .......................417 1.1 Definition of 6(x) .................................417 1.2 Examples of Functions Which Tend to 5(x) ..........418 1.3 Properties of б(х) ................................419 2 Distributions ...........................................420 2.1 The Space S .....................................420 XXII Contents 2.2 Linear Functionate ................................420 2.3 Derivative of a Distribution ........................421 2.4 Convolution Product ..............................422 3 Fourier Transformation ..................................422 3.1 Definition .......................................422 3.2 Fourier Transform of a Gaussian ...................423 3.3 Inversion of the Fourier Transformation .............423 3.4 Parseval-Plancherel Theorem ......................424 3.5 Fourier Transform of a Distribution .................425 3.6 Uncertainty Relation ..............................426 Exercises ..................................................427 Appendix C. Operators in Infinite-Dimensional Spaces ......429 1 Matrix Elements of an Operator ..........................429 2 Continuous Bases .......................................430 Appendix D. The Density Operator .........................435 1 Pure States ............................................436 1.1 A Mathematical Tool: the Trace of an Operator ......436 1.2 The Density Operator of Pure States ...............437 1.3 Alternative Formulation of Quantum Mechanics for Pure States ...................................438 2 Statistical Mixtures .....................................439 2.1 A Particular Case: an Unpolarized Spin-1/2 System .. 439 2.2 The Density Operator for Statistical Mixtures ........440 3 Examples of Density Operators ...........................441 3.1 The Micro-Canonical and Canonical Ensembles ......441 3.2 The Wigner Distribution of a Spinless Point Particle .. 442 4 Entangled Systems .....................................444 4.1 Reduced Density Operator ........................444 4.2 Evolution of a Reduced Density Operator ...........444 4.3 Entanglement and Measurement ....................445 Further Reading ............................................446 Exercises ..................................................446 Solutions to the Exercises ....................................449 Index .........................................................503
any_adam_object	1
author	Basdevant, Jean-Louis 1939- Dalibard, Jean 1958-
author_GND	(DE-588)133559130 (DE-588)121510824
author_facet	Basdevant, Jean-Louis 1939- Dalibard, Jean 1958-
author_role	aut aut
author_sort	Basdevant, Jean-Louis 1939-
author_variant	j l b jlb j d jd
building	Verbundindex
bvnumber	BV022485796
classification_rvk	UK 1000
classification_tum	PHY 020f
ctrlnum	(OCoLC)634405632 (DE-599)BVBBV022485796
discipline	Physik
edition	Corr. 2. print.
format	Book
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genre	(DE-588)4123623-3 Lehrbuch gnd-content
genre_facet	Lehrbuch
id	DE-604.BV022485796
illustrated	Illustrated
indexdate	2024-12-20T12:56:27Z
institution	BVB
isbn	3540277064 9783540277064
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-015693108
oclc_num	634405632
open_access_boolean
owner	DE-384 DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-526 DE-19 DE-BY-UBM DE-29T
owner_facet	DE-384 DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-526 DE-19 DE-BY-UBM DE-29T
physical	XXII, 511 S. Ill., graph. Darst. 1 CD-Rom (12 cm)
publishDate	2005
publishDateSearch	2005
publishDateSort	2005
publisher	Springer
record_format	marc
spellingShingle	Basdevant, Jean-Louis 1939- Dalibard, Jean 1958- Quantum mechanics with 92 exercises with solutions Quantenmechanik (DE-588)4047989-4 gnd
subject_GND	(DE-588)4047989-4 (DE-588)4123623-3
title	Quantum mechanics with 92 exercises with solutions
title_auth	Quantum mechanics with 92 exercises with solutions
title_exact_search	Quantum mechanics with 92 exercises with solutions
title_full	Quantum mechanics with 92 exercises with solutions Jean-Louis Basdevant ; Jean Dalibard
title_fullStr	Quantum mechanics with 92 exercises with solutions Jean-Louis Basdevant ; Jean Dalibard
title_full_unstemmed	Quantum mechanics with 92 exercises with solutions Jean-Louis Basdevant ; Jean Dalibard
title_short	Quantum mechanics
title_sort	quantum mechanics with 92 exercises with solutions
title_sub	with 92 exercises with solutions
topic	Quantenmechanik (DE-588)4047989-4 gnd
topic_facet	Quantenmechanik Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015693108&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT basdevantjeanlouis quantummechanicswith92exerciseswithsolutions AT dalibardjean quantummechanicswith92exerciseswithsolutions

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