.

0 (hodnocen0 x )

BK

EB

First edition

Prague : Charles University, Karolinum Press, 2017

iv, 201 stran : ilustrace (některé barevné) ; 25 cm

ISBN 978-80-246-2321-4 (brožováno)

ISBN 978-80-246-2349-8 (online ; pdf)

Na titulní straně a v tiráži je chybné vročení (datum vydání dotisku 2017), správně je: 2013

Popsáno podle dotisku z roku 2017

001473013

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- particle 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 ? -> 0 108 // Ehrenfest theorem. Role of dccohcrence ...109 // 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 & Hartrec-Fock method ...189 // Bosonic condensates & Hart ree-Bose method ...192 // Pairing & BCS method ...193 // Quantum gases ...198

(OCoLC)862712641

cnb002484419