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Lectures On Quantum Mechanics And Attractors [Kõva köide]

(Inst For Information Transmission Problems Of Russian Academy Of Sciences, Russia)
  • Formaat: Hardback, 272 pages
  • Ilmumisaeg: 30-Mar-2022
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811248893
  • ISBN-13: 9789811248894
Teised raamatud teemal:
Lectures On Quantum Mechanics And AttractorsSuurem pilt
  • Formaat: Hardback, 272 pages
  • Ilmumisaeg: 30-Mar-2022
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811248893
  • ISBN-13: 9789811248894
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9789811248894.html
Märksõnad:
This book gives a concise introduction to Quantum Mechanics with a systematic, coherent, and in-depth explanation of related mathematical methods from the scattering theory and the theory of Partial Differential Equations.The book is aimed at graduate and advanced undergraduate students in mathematics, physics, and chemistry, as well as at the readers specializing in quantum mechanics, theoretical physics and quantum chemistry, and applications to solid state physics, optics, superconductivity, and quantum and high-frequency electronic devices.The book utilizes elementary mathematical derivations. The presentation assumes only basic knowledge of the origin of Hamiltonian mechanics, Maxwell equations, calculus, Ordinary Differential Equations and basic PDEs. Key topics include the Schrödinger, Pauli, and Dirac equations, the corresponding conservation laws, spin, the hydrogen spectrum, and the Zeeman effect, scattering of light and particles, photoelectric effect, electron diffraction, and relations of quantum postulates with attractors of nonlinear Hamiltonian PDEs. Featuring problem sets and accompanied by extensive contemporary and historical references, this book could be used for the course on Quantum Mechanics and is also suitable for individual study.
Preface vii
Introduction xvii
I Nonrelativistic Quantum Mechanics
1(42)
I.1 Photons and Wave-Particle Duality
2(5)
I.1.1 Planck's law and Einstein's photons
2(1)
I.1.2 De Broglie's wave-particle duality
3(4)
I.2 The Schrodinger Equation
7(6)
I.2.1 Canonical quantization
7(2)
I.2.2 Quasiclassical asymptotics and geometrical optics
9(4)
I.3 Quantum Observables
13(10)
I.3.1 Hamiltonian structure
13(1)
I.3.2 Charge and current densities
14(1)
I.3.3 Quantum momentum and angular momentum
15(1)
I.3.4 Correspondence principle
16(1)
I.3.5 Conservation laws
16(2)
I.3.6 Proof of conservation laws
18(2)
I.3.7 The Heisenberg picture
20(1)
I.3.8 Plane waves as electron beams
21(1)
I.3.9 The Heisenberg uncertainty principle
22(1)
I.4 Bohr's postulates
23(4)
I.4.1 Schrodinger's identification of stationary orbits
24(1)
I.4.2 Perturbation theory
25(2)
I.5 Coupled Maxwell--Schrodinger Equations
27(2)
I.6 Hydrogen Spectrum
29(8)
I.6.1 Spherical symmetry and separation of variables
30(3)
I.6.2 Spherical coordinates
33(1)
I.6.3 Radial equation
34(2)
I.6.4 Eigenfunctions
36(1)
I.7 Spherical Eigenvalue Problem
37(6)
I.7.1 The Hilbert--Schmidt argument
37(1)
I.7.2 The Lie algebra of quantum angular momenta
38(1)
I.7.3 Irreducible representations
38(2)
I.7.4 Spherical harmonics. Proof of Theorem 1.6.6
40(1)
I.7.5 Angular momentum in spherical coordinates
41(2)
II Scattering of Light and Particles
43(38)
II.1 Classical Scattering of Light
44(5)
II.1.1 Incident wave
44(1)
II.1.2 The Thomson scattering
45(1)
II.1.3 Neglecting the selfaction
45(2)
II.1.4 Dipole approximation
47(2)
II.2 Quantum Scattering of Light
49(4)
II.2.1 Scattering problem
49(1)
II.2.2 Atomic form factor
49(3)
II.2.3 Energy flux
52(1)
II.3 Polarization and Dispersion
53(6)
II.3.1 First-order approximation
53(2)
II.3.2 Limiting amplitudes
55(1)
II.3.3 The Kramers--Kronig formula
56(3)
II.4 Photoelectric Effect
59(8)
II.4.1 Resonance with the continuous spectrum
61(1)
II.4.2 Limiting amplitude
62(2)
II.4.3 Angular distribution: the Wentzel formula
64(1)
II.4.4 Derivation of Einstein's rules
64(2)
II.4.5 Further improvements
66(1)
II.5 Classical Scattering of Charged Particles
67(3)
II.5.1 The Kepler problem
67(1)
II.5.2 Angle of scattering
68(1)
II.5.3 The Rutherford scattering
69(1)
II.6 Quantum Scattering of Electrons
70(4)
II.6.1 Radiated outgoing wave
70(2)
II.6.2 Differential cross section
72(2)
II.7 Electron Diffraction
74(7)
II.7.1 Introduction
74(1)
II.7.2 Electron diffraction
74(3)
II.7.3 Limiting absorption principle
77(1)
II.7.4 The Fraunhofer asymptotics
78(1)
II.7.5 Comparison with experiment
79(2)
III Atom in Magnetic Field
81(24)
III.1 Normal Zeeman Effect
82(3)
III.1.1 Magnetic Schrodinger equation
82(1)
III.1.2 Selection rules
83(2)
III.2 Intrinsic Magnetic Moment of Electrons
85(4)
III.2.1 The Einstein--de Haas experiment
85(2)
III.2.2 The Lande vector model
87(1)
III.2.3 The Stern--Gerlach experiment
87(1)
III.2.4 The Goudsmit--Uhlenbeck hypothesis
87(2)
III.3 Spin and the Pauli Equation
89(9)
III.3.1 Uniform magnetic field
89(2)
III.3.2 General Maxwell field
91(1)
III.3.3 The Maxwell--Pauli equations
91(1)
III.3.4 Rotation group and angular momenta
92(1)
III.3.5 Rotational covariance
93(2)
III.3.6 Conservation laws
95(3)
III.4 Anomalous Zeeman Effect
98(7)
III.4.1 Spin-orbital coupling
98(1)
III.4.2 Gyroscopic ratio
99(1)
III.4.3 Quantum numbers
100(1)
III.4.4 The Lande formula
101(2)
III.4.5 Applications of the Lande formula
103(2)
IV Relativistic Quantum Mechanics
105(32)
IV.1 Free Dirac Equation
106(3)
IV.2 The Pauli Theorem
109(2)
IV.3 The Lorentz Covariance
111(2)
IV.4 Angular Momentum
113(3)
IV.5 Negative Energies
116(2)
IV.6 Coupling to the Maxwell Field
118(3)
IV.6.1 Gauge invariance
118(1)
IV.6.2 Antiparticles
119(2)
IV.7 Charge and Current. Continuity Equation
121(1)
IV.8 Nonrelativistic Limits
122(4)
IV.8.1 Order 1/c
123(1)
IV.8.2 Order 1/c2
124(2)
IV.9 The Hydrogen Spectrum
126(11)
IV.9.1 Spinor spherical functions
129(4)
IV.9.2 Separation of variables
133(1)
IV.9.3 Factorization method
134(3)
V Quantum Postulates and Attractors
137(20)
V.1 Quantum Jumps
138(3)
V.1.1 Quantum jumps as global attraction
138(1)
V.1.2 Einstein--Ehrenfest's paradox. Bifurcation of attractors
139(2)
V.2 Conjecture on Attractors
141(8)
V.2.1 Trivial symmetry group G = {e}
142(2)
V.2.2 Symmetry group of translations G = Rn
144(1)
V.2.3 Unitary symmetry group G = U{1)
145(1)
V.2.4 Orthogonal symmetry group G = SO(3)
146(1)
V.2.5 Generic equations
146(1)
V.2.6 Empirical evidence
147(2)
V.3 Wave-Particle Duality
149(5)
V.3.1 Reduction of wave packets
149(1)
V.3.2 Diffraction of electrons
150(1)
V.3.3 Quasiclassical asymptotics for the electron gun
150(4)
V.4 Probabilistic Interpretation
154(3)
V.4.1 Diffraction current
154(1)
V.4.2 Discrete registration of electrons
155(1)
V.4.3 Superposition principle as a linear approximation
156(1)
VI Attractors of Hamiltonian PDEs
157(46)
VI.1 Global Attractors of Nonlinear PDEs
158(3)
VI.2 Global Attraction to Stationary States
161(9)
VI.2.1 The d'Alembert equation
161(1)
VI.2.2 String coupled to a nonlinear oscillator
162(3)
VI.2.3 String coupled to several nonlinear oscillators
165(1)
VI.2.4 Nonlinear string
165(1)
VI.2.5 Wave-particle system
166(2)
VI.2.6 Coupled Maxwell--Lorentz equations
168(2)
VI.3 Soliton-Like Asymptotics
170(5)
VI.3.1 Global attraction to solitons
170(1)
VI.3.2 Adiabatic effective dynamics
171(2)
VI.3.3 Mass-energy equivalence
173(2)
VI.4 Global Attraction to Stationary Orbits
175(20)
VI.4.1 Nonlinear Klein--Gordon equation
175(2)
VI.4.2 Generalizations and open questions
177(1)
VI.4.3 Omega-limit trajectories
178(2)
VI.4.4 Limiting absorption principle
180(3)
VI.4.5 Nonlinear analog of the Kato theorem
183(3)
VI.4.6 Dispersive and bound components
186(1)
VI.4.7 Omega-compactness
186(2)
VI.4.8 Reduction of spectrum to spectral gap
188(1)
VI.4.9 Reduction of spectrum to a single point
189(2)
VI.4.10 Nonlinear radiative mechanism
191(4)
VI.5 Numerical Simulation of Soliton Asymptotics
195(8)
VI.5.1 Kinks of relativistic Ginzburg--Landau equations
195(1)
VI.5.2 Numerical simulation
195(4)
VI.5.3 Soliton asymptotics
199(1)
VI.5.4 Adiabatic effective dynamics
199(4)
Appendix A Old Quantum Theory
203(14)
A.1 Black-body radiation law
203(1)
A.2 The Thomson electron and the Lorentz theory
204(1)
A.3 The Zeeman effect
205(1)
A.4 Debye's quantization rule
206(1)
A.5 Correspondence principle and selection rules
207(1)
A.6 The Bohr--Sommerfeld quantization
208(2)
A.7 Atom in magnetic field
210(4)
A.7.1 Rotating frame of reference. Larmor's theorem
211(1)
A.7.2 Spatial quantization
212(2)
A.8 Normal Zeeman effect
214(1)
A.9 The Bohr--Pauli theory of periodic table
215(1)
A.10 The Hamilton--Jacobi and eikonal equations
216(1)
Appendix B The Noether Theory of Invariants
217(4)
Appendix C Perturbation Theory
221(2)
Bibliography 223(16)
Index 239