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0 (hodnocen0 x )

EB

EB

ONLINE

[Praha] : Karolinum, 2025

1 online zdroj (282 stran)

ISBN 978-80-246-6128-5 (online ; pdf)

ISBN 978-80-246-6127-8 (print)

The book represents a concise summary of non-relativistic quantum theory and its applications on the level suitable for university students of physics. It is intended as a supplement to an intensive one-year course of quantum theory, requiring basic knowledge of calculus, algebra, classical mechanics and a bit of motivation for the quantum adventure. It may also be used by more advanced students as a compact overview. The exposition is succinct, with minimal narration, but with a maximum of explicit and hierarchically structured mathematical derivations.The book covers all essential topics of basic quantum mechanics – from general mathematical formalism to specific applications. The formulation of quantum theory is accompanied by illustrations of the general concepts in elementary systems. Some subtleties of mathematical foundations are overviewed, but the formalism is used in an accessible, intuitive way. Besides the traditional topics – such as single-particle dynamics, symmetries, theory of angular momentum, density-matrix formalism, perturbative approximations, scattering theory, description of many-body systems – the course also touches upon some modern issues, including quantum entanglement, decoherence, measurement, nonlocality, artificial systems and quantum information. Historical context is outlined in brief remarks.The second revised and extended edition provides more detailed and user-friendly presentations and also new explanations and themes. It offers a more balanced and comprehensible introduction to both traditional topics and modern developments in quantum theory..

002002071

Preface and comments to 1st & 2nd editions. Literature 1 // Rough guide to notation 4 // Distant outline of quantum physics ...6 // Introduction ...9 // Quantum level. Double-slit experiment ...9 // Wavefunction. Superposition & interference ...11 // Quantum measurement ...13 // 1a. Space of quantum states ...15 // Hilbert space & rigged Hilbert space ...15 // Dirac notation. Linear operators & projectors ...18 // Sums & products of spaces. Composite systems & entangled states ...20 // 1b. Examples of quantum Hilbert spaces // Single structureless particle with spin 0 or Ensembles of distinguishable particles // Indistinguishable particles. Bosons & fermions. Fock space // Artificial systems // 2a. Representation of quantum observables 32 // Operators associated with observables ...32 // Eigenvalues & eigenvectors in finite & infinite dimension ...34 // Probability of measurement outcomes ...41 // 2b. Examples of quantum observables ...42 // Coordinate & momentum ...43 // Hamiltonian of free particle & particle in potential ...44 // Orbital angular momentum. Isotropic Hamiltonians ...48 // Hamiltonian of a particle in electromagnetic field ...53 // Hamiltonians of simple coupled systems ...55 // 3a. Compatible and incompatible observables 57 // Compatible observables. Complete set ...57 // Incompatible observables. Uncertainty relation ...59 // Analogy with Poisson brackets ...60 // 11 // Equivalent representations ...61 // 3b. Examples of observable sets ...63 // Coordinate & momentum. Ladder operators ...63 // Coordinate & momentum representations ...66 // Angular momentum operators ...68 // Addition of two or more angular momenta ...71 // Complete sets of commuting operators for structureless particle ...76 // 4a. Representation of physical transformations 77 // Properties of unitary operators ...78 // Canonical & symmetry transformations ...79 //

Fundamentals of group theory ...82 // 4b. Examples of symmetry transformations 86 // Space translation ...86 // Space rotation ...88 // Irreducible representations of the rotation group ...92 // Spherical tensor operators ...94 // Space inversion ...97 // Time translation & reversal. Galilean transformations ...98 // Symmetry and degeneracy ...101 // 5a. Unitary time evolution 103 // Evolution operator & Schrödinger equation ...103 // Single-particle probability current ...104 // Conservation laws & symmetries ...107 // Energy x time uncertainty ...108 // Hamiltonians depending on time. Dyson series ...112 // Schrödinger, Heisenberg & Dirac description ...113 // Green operator. Single-particle propagator ...115 // 5b. Examples of unitary evolution 118 // Two-level system ...118 // Free particle ...119 // Coherent states in harmonic oscillator. Ehrenfest theorem ...121 // Spin in rotating magnetic field ...124 // 6a. Quantum statistical ensembles 126 // Density operator. Generalized quantum states ...126 // Entropy. Canonical ensemble ...129 // Wigner quasiprobability distribution ...131 // Density operator for open systems ...132 // Evolution of density operator: closed & open systems ...135 // 6b. Examples of statistical ensembles 138 // Harmonic oscillator at nonzero temperature ...138 // Coherent superposition vs. statistical mixture ...139 // Density operator and decoherence for a two-state system ...140 // 7a. Quantum measurement 143 // State vector reduction. Interpretation problems ...143 // A model of measurement. Repeated measurements ...146 // Measurements on entangled states. EPR situation ...149 // Quantum nonlocality & Bell inequalities ...153 // 7b. Examples of quantum measurements ...156 // Destructive & nondestructive measurements ...156 // Production & measurement of entangled states ...158 // 8. Links between Quantum and Classical ...160 //

Classical limit of quantum theory ...160 // Feynman integral. Aharonov-Bohm effect. Level density ...164 // Semiclassical approximation ...169 // 9. Quantum information 174 // Quantum information channel ...175 // Quantum computation ...176 // 10. Stationary approximation methods 181 // Variational method ...181 // Stationary perturbation method ...184 // Application in atomic physics ...189 // Application to level dynamics ...193 // 11. Nonstationary approximation methods 197 // Nostationary perturbation method ...197 // Application to stimulated electromagnetic transitions ...203 // Driven systems ...207 // 12. Scattering: Iterative approaches 210 // Elementary description of elastic scattering ...211 // IV // General formalism: Lippmann-Schwinger equation ...215 // Application to elastic scattering ...219 // 13. Scattering: Partial waves 222 // Elastic scattering via partial waves ...223 // Inclusion of inelastic scattering ...229 // Low-energy & resonance scattering ...232 // 14. Bosonic & Fermionic systems 234 // Hilbert space of bosons & fermions ...234 // Bosonic & fermionic creation/annihilation operators ...235 // Operators in bosonic & fermionic TV-particle spaces ...241 // Quantization of electromagnetic field ...247 // 15. Many-body techniques 249 // Fermionic mean field & Hartree-Fock method ...249 // Bosonic condensates & Hartree-Bose method ...253 // Pairing & BCS method ...254 // Quantum gases ...259 // Concluding words 266 // Index 267