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Bibliografická citace

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EB
EB
ONLINE
1. elektronické vydání
Karolinum 2015
1 online zdroj (210 stran)
Externí odkaz    Plný text PDF (Bookport) 
   * Návod pro Bookport 


ISBN 978-80-246-2349-8 (online ; pdf)
ISBN 978-80-246-2321-4 (print)
This book represents a concise summary of non-relativistic quantum mechanics on the level suitable for university students of physics. It covers, perhaps even slightly exceeds, a one-year course of about 50 lectures, requiring basic knowledge of calculus, algebra, classical mechanics and a bit of motivation for the quantum adventure.The exposition is succinct, with minimal narration, but with a maximum of explicit and hierarchically structured mathematical derivations. The text covers all essential topics of university courses of quantum mechanics – from general mathematical formalism to specific applications. The formulation of quantum theory is accompanied by illustrations of the general concepts of elementary quantum systems. Some subtleties of mathematical foundations are overviewed, but the formalism is used in an accessible, intuitive way. Besides the traditional topics of non-relativistic quantum mechanics, such as single-particle dynamics, symmetries, semiclassical and perturbative approximations, density-matrix formalism, scattering theory, theory of angular momentum, description of many-particle systems – the course also touches upon some modern issues, including quantum entanglement, decoherence, measurement, nonlocality, and quantum information. Historical context and chronology of basic achievements is outlined in brief remarks. The book is intended for beginners as a supplement to lectures, however, it may also be used by more advanced students as a compact and comprehensible overview of elementary quantum theory..
001489396
Contents // Preface 1 // Rough guide to notation 3 // INTRODUCTION 5 // 1. FORMALISM 2. SIMPLE SYSTEMS 10 // 1.1 Space of quantum states... 10 // Hilbert space. Rigged Hilbert space...10 // Dirac notation...12 // Sum & product of spaces... 14 // 2.1 Examples of quantum Hilbert spaces...15 // Single structureless particle with spin 0 or  ...15 // 2 distinguishable/indistinguishable particles. Bosons & fermions ... 17 Ensembles of A > 2 particles ...19 // 1.2 Representation of observables...21 // Observables as Hermitian operators. Basic properties...21 // Eigenvalues & eigenvectors in finite & infinite dimension...23 // Discrete & continuous spectrum. Spectral decomposition...25 // 2.2 Examples of quantum operators...27 // Spin-1 operators...27 // Coordinate & momentum ...29 // Hamiltonian of free particle ? part icle in potential...30 // Orbital angular momentum. Isotropic Hamiltonians...33 // Hamiltonian of a particle in electromagnetic field ...37 // 1.3 Compatible and incompatible observables...39 // Compat ible observables. Complete set ...39 // Incompatible observables. Uncertainty relation...41 // Analogy with Poisson brackets...42 // Equivalent representations...43 // 2.3 Examples of commuting ? noncommuting operators...44 // Coordinate, momentum & associated representations...44 // Angular momentum components...47 // Complete sets of commuting operators for structureless particle ... 49 // 1.4 Representation of physical transformations...50 // Properties of unitary operators
...50 // Canonical ? symmetry transformations...52 // Basics of group theory...54 // 2.4 Fundamental spatio-temporal symmetries...56 // Space translation...57 // Space rotation... // Space inversion...gl // Time translation & reversal. Galilean transformations...62 // Symmetry & degeneracy...64 // 1.5 Unitary evolution of quantum systems...65 // Nonstationary Schrödinger equation. Flow. Continuity equation. ... 65 // Conservation laws ? symmetries...67 // Energy x time uncertainty. (Non)exponential decay...68 // Hamiltonians depending on time. Dyson scries...71 // Schrödinger, Heisenberg ? Dirac description...73 // Green operator. Single-particle propagator...74 // 2.5 Examples of quantum evolution...76 // Two-level system...76 // Free particle... // Coherent states in harmonic oscillator... 79 // Spin in rotating magnetic field...81 // 1.6 Quantum measurement...83 // State vector reduction ? consequences...83 // EPR situation. Interpretation problems...85 // 2.6 Implications ? applications of quantum measurement...89 // Paradoxes of quantum measurement...89 // Applications of quantum measurement...91 // Hidden variables. Bell inequalities. Nonlocality ...92 // 1.7 Quantum statistical physics...94 // Pure and mixed states. Density operator...95 // Entropy. Canonical ensemble ...96 // Wigner distribution function...gg // Density operator for open systems...99 // Evolution of density operator: closed ? open systems...101 // 2.7 Examples of statistical description ...104 // Harmonic
oscillator at nonzero temperature...104 // Coherent superposition vs. statistical mixture...105 // Density operator and decohercnce for a two-state system...106 // 3. QUANTUM-CLASSICAL CORRESPONDENCE 108 // 3.1 Classical limit of quantum mechanics...108 // The limit ? -> 0 ?8 // Ehrenfest theorem. Role of dccohcrence...109 // iii // 3.2 WKB approximation...112 // Classical Hamilton-Jacobi theory...112 // WKB equations ? interpretation...114 // Quasiclassical approximation...115 // 3.3 Feynman integral...118 // Formulation of quantum mechanics in terms of trajectories..118 // Application to the Aharonov-Bohm effect...119 // Application to the density of states...120 // 4. ANGULAR MOMENTUM 123 // 4.1 General features of angular momentum...123 // Eigenvalues and ladder operators...123 // Addition of two angular momenta...125 // Addition of three angular momenta...128 // 4.2 Irreducible tensor operators...129 // Euler angles. Wigner functions. Rotation group irreps...129 // Spherical tensors. Wigner-Eckart theorem ...130 // 5. APPROXIMATION TECHNIQUES 133 // 5.1 Variational method...133 // Dynamical ? stationary variational principle. Ritz method...133 // 5.2 Stationary perturbation method...136 // General setup ? equations...136 // Nondegenerate case...138 // Degenerate case...139 // Application in atomic physics...141 // Application to level dynamics...145 // Driven systems. Adiabatic approximation ...147 // 5.3 Nonstationary perturbation method...149 // General formalism ...149
// Step perturbation...152 // Exponential ? periodic perturbations...154 // Application to stimulated electromagnetic transitions...155 // 6. SCATTERING THEORY 157 // 6.1 Elementary description of elastic scattering...158 // Scattering by fixed potential. Cross section...158 // Two-body problem. Center-of-mass system...159 // Effect of particle indistinguishability in cross section...160 // 6.2 Perturbative approach the scattering problem...161 // IV // Lippmann-Schwinger equation...161 // Born series for scattering amplitude...164 // 6.3 Method of partial waves...166 // Expression of elastic scattering in terms of spherical waves..166 // Inclusion of inelastic scattering ...172 // Low-energy & resonance scattering...174 // 7. MANY-BODY SYSTEMS 175 // 7.1 Formalism of particle creation/annihilation operators...176 // Hilbert space of bosons & fermions...176 // Bosonic & fermionic creation/annihilation operators...177 // Operators in bosonic & fermionic A-particle spaces...181 // Quantization of elect romagnetic field...186 // 7.2 Many-body techniques...189 // Fermionic mean field & Hartrcc-Fock method ...189 // Bosonic condensates & Hart ree-Bose method...192 // Pairing & BCS method...193 // Quantum gases...198 // // // / // \\ ***•. ? // // // \\ // HEALTH flUTHORITX WARNij 1 // THINKING ABOUT’ QUANTUM ???51?5

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