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E-grāmata: Lectures on Quantum Mechanics: With Problems, Exercises and Solutions

  • Formāts: EPUB+DRM
  • Sērija : Graduate Texts in Physics
  • Izdošanas datums: 02-Feb-2023
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783031176357
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Lectures on Quantum Mechanics: With Problems, Exercises and SolutionsPalielināt
  • Formāts: EPUB+DRM
  • Sērija : Graduate Texts in Physics
  • Izdošanas datums: 02-Feb-2023
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783031176357
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The new edition of this remarkable textbook offers the reader a conceptually strong introduction to quantum mechanics, but goes beyond this to present a fascinating tour of modern theoretical physics. Beautifully illustrated and engagingly written, it starts with a brief overview of diverse topics across physics including nanotechnology, materials science, and cosmology. It provides new chapters on astrophysics, quantum information and the photon. Each chapter provides a set of exercises, questions, a problem and solutions.

The core of the book covers both established and emerging aspects of quantum mechanics. A concise introduction to traditional quantum mechanics covers the Schrödinger equation, Hilbert space, photon physics, the algebra of observables, hydrogen atom, spin and Pauli principle. Modern features of the field are presented with Bell's inequality by exploring systems of entangled states, that have generated the 'second quantum revolution' of systems that communicate instantly at a distance, and the birth of quantum information: cryptography, teleportation and quantum computers.
1 Perception and Imagination
1(8)
1.1 Physics and Language
2(1)
1.2 The Infinitely Complex
2(1)
1.3 The Paradoxes and the Second Revolution
3(2)
1.4 Plan of the Text
5(2)
1.5 Physical Constants
7(2)
2 Quantum Phenomena
9(24)
2.1 Planck's Quanta
10(4)
2.1.1 Einstein and the Photon
12(1)
2.1.2 Atomic Spectroscopy and Bohr's Model
12(2)
2.2 Wave Behavior of Particles
14(4)
2.2.1 Interferences
14(1)
2.2.2 Wave Behavior of Matter
15(2)
2.2.3 Analysis of the Phenomenon
17(1)
2.3 Probabilistic Nature of Quantum Phenomena
18(3)
2.3.1 Random Behavior of Particles
18(1)
2.3.2 A Nonclassical Probabilistic Phenomenon
18(1)
2.3.3 Conclusions
19(2)
2.4 Phenomenological Description, de Broglie Waves
21(1)
2.5 First Discovery, Applications
22(2)
2.6 Appendix: Notions on Probabilities
24(7)
2.7 Exercises
31(2)
3 Wave Function, Schrddinger Equation
33(30)
3.1 Terminology and Methodology
33(2)
3.2 Principles of Wave Mechanics
35(3)
3.2.1 The Wave Function
35(1)
3.2.2 Schrodinger Equation in Presence of a Potential --
36(2)
3.3 Superposition Principle
38(1)
3.4 Wave Packets
39(3)
3.4.1 Free Wave Packets
39(1)
3.4.2 Fourier Transforms
39(2)
3.4.3 Shape of Wave Packets
41(1)
3.5 Historical Landmarks
42(1)
3.6 Momentum Probability Law
43(3)
3.6.1 Free Particle
43(1)
3.6.2 General Case
44(2)
3.7 Heisenberg Uncertainty Relations
46(4)
3.8 Controversies and Paradoxes
50(1)
3.9 Appendix. Dirac S "Function", Distributions
51(5)
3.10 Appendix: Fourier Transformation
56(4)
3.11 Exercises
60(3)
References
61(2)
4 Physical Quantities and Measurement
63(18)
4.1 Statement of the Problem
64(2)
4.1.1 Physical Quantities
64(1)
4.1.2 Position and Momentum
65(1)
4.2 Observables
66(3)
4.2.1 Position and Momentum Observables
67(1)
4.2.2 Correspondence Principle
68(1)
4.2.3 Historical Landmarks
68(1)
4.3 A Counterexample of Einstein and Its Consequences
69(6)
4.3.1 What Do We Know After a Measurement?
71(1)
4.3.2 Eigenstates and Eigenvalues of an Observable
72(1)
4.3.3 Wave Packet Reduction
73(1)
4.3.4 Decoherence
74(1)
4.4 Schrodinger's Cat Paradox
75(5)
4.5 Exercises
80(1)
References
80(1)
5 Energy, Quantization and Quantum Tunneling
81(26)
5.1 Energy and Time Dependence
81(4)
5.1.1 The Hamiltonian
81(2)
5.1.2 The Schrodinger Equation, Time and Energy
83(1)
5.1.3 Stationary States
84(1)
5.1.4 Motion: Interference of Stationary States
84(1)
5.2 Simple Systems
85(2)
5.2.1 Bound States and Scattering States
86(1)
5.2.2 One-Dimensional Problems
87(1)
5.3 The Harmonic Oscillator
87(2)
5.4 Square Well Potentials
89(6)
5.5 Crossing a Potential Barrier, Tunnel Effect
95(1)
5.6 Applications of the Tunnel Effect
96(3)
5.6.1 Valence Electrons
98(1)
5.7 Nanotechnologies
99(4)
5.8 Exercises
103(2)
5.9 Problem. The Ramsauer effect
105(2)
5.9.1 Solution
106(1)
6 Principles of Quantum Mechanics
107(24)
6.1 Hilbert Space
108(4)
6.2 Dirac Formalism
112(4)
6.2.1 Notations
112(2)
6.2.2 Operators
114(1)
6.2.3 Syntax Rules
115(1)
6.2.4 Projectors; Decomposition of the Identity
115(1)
6.3 Measurement Results
116(5)
6.3.1 Eigenvectors and Eigenvalues of an Observable
116(1)
6.3.2 Results of the Measurement of a Physical Quantity
117(1)
6.3.3 Probabilities
118(1)
6.3.4 The Riesz Spectral Theorem
119(1)
6.3.5 Physical Meaning of Various Representations
120(1)
6.4 Principles of Quantum Mechanics
121(2)
6.4.1 The Case of a Continuous Spectrum
122(1)
6.5 Heisenberg's matrices
123(4)
6.6 Exercises
127(4)
Reference
129(2)
7 Two-State Systems, Matrix Mechanics
131(34)
7.1 Double Well, the Ammonia Molecule
131(8)
7.1.1 The Model
132(1)
7.1.2 Stationary States and Tunneling
133(1)
7.1.3 Energy Levels
134(2)
7.1.4 Wave Functions
136(1)
7.1.5 Inversion of the Molecule
136(3)
7.2 "Two-State" System
139(2)
7.3 Matrix Quantum Mechanics
141(4)
7.4 NH3 in an Electric Field
145(3)
7.4.1 Uniform Constant Field
146(1)
7.4.2 Weak and Strong Field Regimes
147(1)
7.4.3 Other Two-State Systems
148(1)
7.5 Motion of the Molecule in an Inhomogeneous Field
148(3)
7.5.1 Force on the Molecule in an Inhomogeneous Field
148(3)
7.5.2 Population Inversion
151(1)
7.6 Reaction to an Oscillating Field, The Maser
151(2)
7.7 Principle and Applications of the Maser
153(5)
7.7.1 Amplifiers
154(1)
7.7.2 Oscillators
155(1)
7.7.3 Atomic Clocks and the GPS
155(1)
7.7.4 Tests of Relativity
156(2)
7.8 Exercises
158(3)
7.9 Problem. Aromatic Molecules
161(4)
7.9.1 Solution
162(3)
8 The Photon
165(20)
8.1 Polarization of Light
165(6)
8.1.1 Polarization States
167(1)
8.1.2 Polarizers at an Angle
168(1)
8.1.3 Polarization States
168(2)
8.1.4 Circular Polarisation
170(1)
8.1.5 Quantum "Logic"
170(1)
8.2 Nature of Photon, Wave or Particle
171(2)
8.3 Interference Experiments
173(4)
8.3.1 Attenuated Light Experiments
174(3)
8.4 Physics with Individual Photons
177(4)
8.4.1 Single Photon Sources
177(2)
8.4.2 Particle Nature of the Photon
179(2)
8.5 Single Photon Interferences
181(1)
8.6 Exercises
182(3)
References
183(2)
9 The Algebra of Observables
185(26)
9.1 Commutation of Observables
186(2)
9.1.1 Fundamental Commutation Relation
186(1)
9.1.2 Other Commutation Relations
186(1)
9.1.3 Dirac in the Summer of 1925
187(1)
9.2 Uncertainty Relations
188(1)
9.3 Evolution of Physical Quantities
189(4)
9.3.1 Evolution of an Expectation Value
189(1)
9.3.2 Particle in a Potential, Classical Limit
190(2)
9.3.3 Conservation Laws
192(1)
9.4 Algebraic Resolution of the Harmonic Oscillator
193(3)
9.5 Commuting Observables
196(5)
9.5.1 Theorem
197(1)
9.5.2 Example
198(1)
9.5.3 Tensor Structure of Quantum Mechanics
198(1)
9.5.4 Complete Set of Commuting Observables (CSCO)
199(1)
9.5.5 Completely Prepared Quantum State
200(1)
9.6 Sunday September 20, 1925
201(2)
9.7 Exercices
203(3)
9.8 Problem. Quasi-Classical States of the Harmonic Oscillator
206(5)
9.8.1 Solution
207(3)
Reference
210(1)
10 Approximation Methods
211(18)
10.1 Perturbation Theory
211(5)
10.1.1 Definition of the Problem
211(2)
10.1.2 First Order Perturbation Theory
213(2)
10.1.3 Second Order Perturbation to the Energy Levels --
215(1)
10.2 The Variational Method
216(3)
10.2.1 The Ground State
216(1)
10.2.2 Example
217(1)
10.2.3 Relation with Perturbation Theory
218(1)
10.2.4 Other Levels
218(1)
10.3 Exercises
219(1)
10.4 Problem. Conductivity of Crystals; Energy Bands
220(9)
10.4.1 Electrons in a Periodic Potential
221(3)
10.4.2 Solution
224(5)
11 Angular Momentum
229(22)
11.1 Fundamental Commutation Relation
230(2)
11.1.1 Classical Angular Momentum
230(1)
11.1.2 Definition of an Angular Momentum Observable
230(1)
11.1.3 Results of the Quantization
231(1)
11.2 Proof of the Quantization
232(4)
11.2.1 Statement of the Problem
232(1)
11.2.2 Vectors | j,m > and Eigenvalues j and m
233(1)
11.2.3 Operators J± = Jx ±iJy
233(2)
11.2.4 Quantization
235(1)
11.3 Orbital Angular Momenta
236(3)
11.3.1 Formulae in Spherical Coordinates
236(1)
11.3.2 Integer Values of m and l
236(1)
11.3.3 Spherical Harmonics
237(2)
11.4 Rotation Energy of a Diatomic Molecule
239(1)
11.5 Interstellar Molecules, the Origin of Life
240(4)
11.6 Angular Momentum and Magnetic moment
244(5)
11.6.1 Classical Model
245(1)
11.6.2 Quantum Transposition
246(1)
11.6.3 Experimental Consequences
247(1)
11.6.4 Larmor Precession
248(1)
11.6.5 What About Half-Integer Values of j and m?
248(1)
11.7 Exercises
249(2)
12 The Hydrogen Atom
251(24)
12.1 Two-Body Problem; Relative Motion
252(2)
12.2 Motion in a Central Potential
254(4)
12.2.1 Separation of the Angular Variables
254(2)
12.2.2 The Radial Quantum Number n'
256(1)
12.2.3 The Principal Quantum Number n
256(1)
12.2.4 Spectroscopic Notation (States s, p, d, f, ...)
257(1)
12.3 The Hydrogen Atom
258(8)
12.3.1 Atomic Units; Fine Structure Constant
258(2)
12.3.2 The Dimensionless Radial Equation
260(2)
12.3.3 Spectrum of Hydrogen
262(1)
12.3.4 Stationary States of the Hydrogen Atom
263(1)
12.3.5 Dimensions and Orders of Magnitude
264(1)
12.3.6 Historical Landmarks
265(1)
12.4 Muonic Atoms
266(3)
12.5 Exercises
269(3)
12.6 Problem. Tritium β Decay and Neutrino Mass
272(3)
12.6.1 Solution
273(1)
Reference
274(1)
13 Spin 1/2
275(38)
13.1 Experimental Results
275(2)
13.2 Spin 1/2 Formalism
277(2)
13.3 Complete Description of a Spin 1/2 Particle
279(2)
13.3.1 Mixed Representation
279(1)
13.3.2 Two-Component Wave Function
279(1)
13.3.3 Observables
280(1)
13.4 Physical Spin Effects
281(1)
13.5 Spin Magnetic Moment
281(1)
13.6 The Stern-Gerlach Experiment
282(1)
13.7 Principle of the Experiment
283(6)
13.7.1 Semi-classical Analysis
283(1)
13.7.2 Experimental Results
284(1)
13.7.3 Explanation of the Stern-Gerlach Experiment
285(2)
13.7.4 Successive Stern-Gerlach Setups
287(1)
13.7.5 Measurement Along an Arbitrary Axis
288(1)
13.8 The Discovery of Spin
289(6)
13.8.1 The Hidden Sides of the Stern-Gerlach Experiment
289(2)
13.8.2 Einstein and Ehrenfest's Objections
291(1)
13.8.3 Anomalous Zeeman Effect
292(1)
13.8.4 Bohr's Challenge to Pauli
293(1)
13.8.5 The Spin Hypothesis
293(1)
13.8.6 The Fine Structure of Atomic Lines
294(1)
13.9 Magnetism, Magnetic Resonance
295(10)
13.9.1 Spin Effects, Larmor Precession
296(1)
13.9.2 Larmor Precession in a Fixed Magnetic Field
296(1)
13.9.3 Rabi's Calculation and Experiment
297(4)
13.9.4 Nuclear Magnetic Resonance
301(2)
13.9.5 Magnetic Moments of Particles
303(2)
13.10 Entertainment: Rotation by 2n of a Spin 1/2
305(1)
13.11 Exercises
306(1)
13.12 Problem. Lorentz Force in Quantum Mechanics
307(6)
13.12.1 Solution
309(2)
References
311(2)
14 Fine and Hyperfine Structure of Spectral Lines
313(28)
14.1 Addition of Angular Momenta
314(8)
14.1.1 A Simple Case: The Addition of Two Spins 1/2
315(3)
14.1.2 Addition of Two Arbitrary Angular Momenta
318(4)
14.2 One-Electron Atoms, Spectroscopic Notations
322(3)
14.2.1 Fine Structure of Monovalent Atoms
322(3)
14.3 Hyperfine Structure; The 21 cm Line of Hydrogen
325(4)
14.3.1 Remarks
327(2)
14.4 Radioastronomy
329(4)
14.5 The 21-cm Line of Hydrogen
333(2)
14.6 The Intergalactic Medium; Star Wars
335(4)
14.7 Exercises
339(2)
15 Identical Particles, The Pauli Principle
341(34)
15.1 Indistinguishability of Two Identical Particles
342(2)
15.1.1 Identical Particles in Classical Physics
342(1)
15.1.2 The Quantum Problem
343(1)
15.1.3 Example of Ambiguities
343(1)
15.2 Two-Particle System; The Exchange Operator
344(3)
15.2.1 The Hilbert Space for the Two-Particle System
344(1)
15.2.2 The Exchange Operator Between Two Identical Particles
345(1)
15.2.3 Symmetry of the States
346(1)
15.3 The Pauli Principle
347(3)
15.3.1 The Case of Two Particles
347(1)
15.3.2 Independent Fermions and Exclusion Principle
348(1)
15.3.3 The Case of N Identical Particles
348(2)
15.4 Physical Consequences of the Pauli Principle
350(10)
15.4.1 Exchange Force Between Two Fermions
350(1)
15.4.2 The Ground State of N Identical Independent Particles
351(1)
15.4.3 Behavior of Fermion and Boson Systems at Low Temperatures
352(2)
15.4.4 Stimulated Emission and the Laser Effect
354(2)
15.4.5 Heisenberg Uncertainty Relations for N Fermions
356(4)
15.5 Exercises
360(1)
15.6 Problem. Pauli Principle and the Aging of Stars
361(14)
15.6.1 White Dwarfs
363(1)
15.6.2 Neutron Stars
364(2)
15.6.3 Mini-Boson Stars
366(1)
15.6.4 Solution
367(8)
16 The Evolution of Systems
375(30)
16.1 Time-Dependent Perturbation Theory
376(4)
16.1.1 Example: A Collision Process
376(2)
16.1.2 Constant Perturbation
378(1)
16.1.3 Sinusoidal Perturbation
379(1)
16.2 Interaction of an Atom with an Electromagnetic Wave
380(6)
16.2.1 The Electric Dipole Approximation
380(1)
16.2.2 Justification of the Electric Dipole Interaction
381(1)
16.2.3 Absorption of Energy by an Atom
382(1)
16.2.4 Selection Rules
383(1)
16.2.5 Spontaneous Emission
384(1)
16.2.6 Control of an Atomic Motion by Light
385(1)
16.3 Decay of a System
386(8)
16.3.1 The Radioactivity of 57Fe
387(2)
16.3.2 The Fermi Golden Rule
389(1)
16.3.3 Orders of Magnitude
390(1)
16.3.4 Behavior for Long Times
391(3)
16.4 The Time-Energy Uncertainty Relation
394(3)
16.4.1 Isolated Systems and Intrinsic Interpretations
394(1)
16.4.2 Interpretation of Landau and Peierls
395(1)
16.4.3 The Einstein-Bohr controversy
396(1)
16.5 Exercises
397(1)
16.6 Problem. Molecular Lasers
398(7)
16.6.1 Solution
401(4)
17 Entangled States. The Way of Paradoxes
405(16)
17.1 The EPR Paradox
407(2)
17.2 The Version of David Bohm
409(8)
17.2.1 Bell's Inequality
411(3)
17.2.2 Experimental Tests
414(3)
17.3 The GHZ Experiment
417(4)
17.3.1 Quantum Situation
418(1)
17.3.2 Local Realistic Situations
419(2)
18 Quantum Information and the Fruits of Entanglement
421(20)
18.1 Quantum Information: How to Take Advantage of an Embarrassment
421(1)
18.2 Quantum Teleportation
422(5)
18.2.1 Bell States
423(4)
18.3 Quantum Cryptography
427(6)
18.4 The Quantum Computer
433(5)
18.5 The Quantum Professions
438(3)
References
440(1)
19 Solutions to the Exercises
441(34)
Index 475
Jean-Louis Basdevant, graduated from Ecole Normale Supérieure (1958-1963), PhD at Strasbourg University (1967). Assistant researcher up to Director of Research at the CNRS (1963-2007), CERN (1970-1972). Professor at the Ecole Polytechnique (1969-2004). Nominated Honorary Professor (2004).
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