krainaksiazek relativistic quantum theory of particles ii 20124304

- znaleziono 26 produktów w 1 sklepie

Relativistic Quantum Theory of Particles. I - 2834690796

348,15 zł

Relativistic Quantum Theory of Particles. I LAP Lambert Academic Publishing

Książki / Literatura obcojęzyczna

This two-volume book series is an attempt to formulate a consistent relativistic quantum theory of interacting charged particles. The major construction will be undertaken in the second volume. Our goal in this first volume is to prepare the reader for that effort. Here we will introduce notation, terminology, and basic ideas of relativistic quantum theories. Our discussion will proceed systematically and, more or less traditionally, from the principle of relativity and postulates of measurements to the renormalization in quantum electrodynamics. This will cover material usually found in textbooks on quantum field theory. However, we will choose particles (rather than fields) as our basic ingredients. Quantum fields will be regarded as mere mathematical tools, which are convenient for building relativistically invariant and cluster separable particle interactions. The reader is expected to have a good grasp of non-relativistic quantum mechanics.

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Relativistic Quantum Mechanics and Quantum Field Theory - 2834684537

198,66 zł

Relativistic Quantum Mechanics and Quantum Field Theory Alpha Science International Ltd

Książki / Literatura obcojęzyczna

"Relativistic Quantum Mechanics and Quantum Field Theory" deals with the single particle relativistic wave equations and the elements of quantum field theory. The Klein-Gordon equation is discussed briefly and elaborately the Dirac equation, its free particle solutions and Feynman's positron theory with a view to emphasize how the intuitive approach of Feynman has enormously simplified the calculations in Quantum Electrodynamics - the interaction of radiation with matter - by the introduction of Feynman diagrams. It is shown that Feynman's approach is equivalent to the other more general approach of quantum field theory and the equivalence of the two approaches has been demonstrated through the S-matrix formalism which leads to the Feynman diagrams by the application of Wick's theorem. How the quantum field theory is stretched beyond quantum electrodynamics to include electro weak interactions and strong interactions and how it leads to the formulation of the standard model of elementary particles are briefly discussed.

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Relativistic Quantum Physics - 2826797639

241,82 zł

Relativistic Quantum Physics Cambridge University Press

Książki / Literatura obcojęzyczna

Quantum physics and special relativity theory were two of the greatest breakthroughs in physics during the twentieth century and contributed to paradigm shifts in physics. This book combines these two discoveries to provide a complete description of the fundamentals of relativistic quantum physics, guiding the reader effortlessly from relativistic quantum mechanics to basic quantum field theory. The book gives a thorough and detailed treatment of the subject, beginning with the classification of particles, the Klein

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Relativistic Quantum Mechanics. Wave Equations - 2834137679

478,59 zł

Relativistic Quantum Mechanics. Wave Equations Springer, Berlin

Książki / Literatura obcojęzyczna

Relativistic Quantum Mechanics - Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. Chapter 1 deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner). The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course.

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Relativistic Quantum Mechanics - 2834683215

809,64 zł

Relativistic Quantum Mechanics MCGRAW-HILL COLLEGE

Książki / Literatura obcojęzyczna

In this text the authors develop a propagator theory of Dirac particles, photons, and Klein-Gordon mesons and per-form a series of calculations designed to illustrate varioususeful techniques and concepts in electromagnetic, weak, andstrong interactions. these include defining and implementingthe renormalization program and evaluating effects of radia-tive corrections, such as the Lamb shift, in low-ordercalculations. The necessary background for the book is pro-vided by a course in nonrelativistic quantum mechanics atthe general level of Schiff's text, QUANTUM MECHANICS.

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Physical Principles of the Quantum Theory - 2826720930

60,25 zł

Physical Principles of the Quantum Theory Dover Childrens Books

Książki / Literatura obcojęzyczna

I. INTRODUCTORY 1. Theory and Experiment 2. The Fundamental Concepts of Quantum Theory a) Wilson Photographs b) "Diffraction of Matter Waves (Davisson and Germer, Thomson, Rupp)" c) The Diffraction of X-Rays d) The Compton-Simon Experiment e) The Collision Experiments of Franck and Hertz II. CRITIQUE OF THE PHYSICAL CONCEPTS OF THE CORPUSCULAR THEORY 1. The Uncertainty Relations 2. Illustrations of the Uncertainty Relations a) Determination of the Position of a Free Particle b) Measurement of the Velocity or Momentum of a Free Particle c) Bound Electrons d) Energy Measurements III. CRITIQUE OF THE PHYSICAL CONCEPTS OF THE WAVE THEORY 1. The Uncertainty Relations for Waves 2. Discussion of an Actual Measurement of the Electromagnetic Field IV. THE STATISTICAL INTERPRETATION OF QUANTUM THEORY 1. Mathematical Considerations 2. Interference of Probabilities 3. Bohr's Concept of Complementarity V. DISCUSSION OF IMPORTANT EXPERIMENTS 1. The C. T. R. Wilson Experiments 2. Diffraction Experiments 3. The Experiment of Einstein and Rupp 4. "Emission, Absorption, and Dispersion of Radiation" a) Application of the Conservation Laws b) Correspondence Principle and the Method of Virtual Charges c) The Complete Treatment of Radiation and Matter 5. Interference and the Conservation Laws 6. The Compton Effect and the Compton-Simon Experiment 7. Radiation Fluctuation Phenomena 8. Relativistic Formulation of the Quantum Theory APPENDIX: THE MATHEMATICAL APPARATUS OF THE QUANTUM THEORY 1. The Corpuscular Concept of Matter 2. The Transformation Theory 3. The Schršdinger Equation 4. The Perturbation Method 5. Resonance between Two Atoms: the Physical Interpretation of the Transformation Matrices 6. The Corpuscular Concept for Radiation 7. Quantum Statistics 8. The Wave Concept for Matter and Radiation: Classical Theory 9. Quantum Theory of Wave Fields 10. Application to Waves of Negative Charge 11. Proof of the Mathematical Equivalence of the Quantum Theory of Particles and of Waves 12. Application to the Theory of Radiation INDEX

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Relativistic Effects in Chemistry - 2834138197

1170,00 zł

Relativistic Effects in Chemistry John Wiley & Sons Inc

Książki / Literatura obcojęzyczna

E = mc2 and the Periodic Table ...RELATIVISTIC EFFECTS IN CHEMISTRY This century's most famous equation, Einstein's special theory of relativity, transformed our comprehension of the nature of time and matter. Today, making use of the theory in a relativistic analysis of heavy molecules, that is, computing the properties and nature of electrons, is the work of chemists intent on exploring the mysteries of minute particles. The first work of its kind, Relativistic Effects in Chemistry details the computational and analytical methods used in studying the relativistic effects in chemical bonding as well as the spectroscopic properties of molecules containing very heavy atoms. The first of two independent volumes, Part A: Theory and Techniques describes the basic techniques of relativistic quantum chemistry. Its systematic five--part format begins with a detailed exposition of Einstein's special theory of relativity, the significance of relativity in chemistry, and the nature of relativistic effects, especially with molecules containing both main group atoms and transition metal atoms. Chapter 3 discusses the fundamentals of relativistic quantum mechanics starting from the Klein--Gordon equation through such advanced constructs as the Breit--Pauli and Dirac multielectron Hamiltonian. Modern computational techniques, of importance with problems involving very heavy molecules, are outlined in Chapter 4. These include the relativistic effective core potentials, ab initio CASSCF, CI, and RCI techniques. Chapter 5 describes relativistic symmetry using the double group symmetry of molecules and the classification of relativistic electronic states and is of special importance to chemists or spectroscopists interested in computing or analyzing electronic states of molecules containing very heavy atoms. An exceptional introduction to one of chemistry's foremost analytical techniques, Relativistic Effects in Chemistry is also evidence of the still unending reverberations of Einstein's revolutionary theory.

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Quantum Field Theory II - 2845290155

315,42 zł

Quantum Field Theory II Springer, Berlin

Książki / Literatura obcojęzyczna

This book takes a pedagogical approach§to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics.§§The first part of the book introduces quantum gravity, without§requiring previous knowledge of general relativity (GR). The necessary§geometrical aspects are derived afresh leading to explicit general Lagrangians§for gravity, including that of general relativity. The quantum aspect of§gravitation, as described by the graviton, is introduced and perturbative§quantum GR is discussed. The Schwinger-DeWitt formalism is developed to compute§the one-loop contribution to the theory and renormalizability aspects of the§perturbative theory are also discussed. This follows by introducing only the§very basics of a non-perturbative, background-independent, formulation of§quantum gravity, referred to as "loop quantum gravity", which gives rise to a§quantization of space.§§In the second part the author introduces supersymmetry and§its consequences. The generation of superfields is represented in detail. Supersymmetric generalizations of Maxwell's§Theory as well as of Yang-Mills field theory, and of the standard model are§worked out. Spontaneous symmetry breaking, improvement of the divergence§problem in supersymmetric field theory, and its role in the hierarchy problem§are covered. The unification of the fundamental constants in a supersymmetric§version of the standard model are then studied. Geometrical aspects necessary§to study supergravity are developed culminating in the derivation of its full§action.§§The third part§introduces string theory and the analysis of the spectra of the mass (squared)§operator associated with the oscillating strings. The properties of the§underlying fields, associated with massless particles, encountered in string§theory are studied in some detail. Elements of compactification, duality and§D-branes are given, as well of the generation of vertices and interactions of§strings. In the final sections, the author shows how to recover GR and the§Yang-Mills field Theory from string theory.§

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Quantum Field Theory - 2826627838

185,47 zł

Quantum Field Theory DOVER PUBLICATIONS

Książki / Literatura obcojęzyczna

Preface General References 1. Classical Theory 1.1 Principle of Least Action 1.1.1 Classical Motion 1.1.2 Electromagnetic Field as an Infinite Dynamical System 1.1.3 Electromagnetic Interaction of a Point Particle 1.2 Symmetries and Conservation Laws 1.2.1 Fundamental Invariants 1.2.2 Energy Momentum Tensor 1.2.3 Internal Symmetries 1.3 Propagation and Radiation 1.3.1 Green Functions 1.3.2 Radiation 2. The Dirac Equation 2.1 Toward a Relativistic Wave Equation 2.1.1 Quantum Mechanics and Relativity 2.1.2 The Dirac Equation 2.1.3 Relativistic Covariance 2.2 Physical Content 2.2.1 Plane Wave Solutions and Projectors 2.2.2 Wave Packets 2.2.3 Electromagnetic Coupling 2.2.4 Foldy-Wouthuysen Transformation 2.3 Hydrogen-like Atoms 2.3.1 Nonrelativistic versus Relativistic Spectrum 2.3.2 Dirac Theory 2.4 Hole Theory and Charge Conjugation 2.4.1 Reinterpretation of Negative Energy Solutions 2.4.2 Charge Conjugation 2.4.3 Zero-Mass Particles 2.5 Dirac Propagator 2.5.1 Free Propagator 2.5.2 Propagation in an Arbitrary External Electromagnetic Field 2.5.3 Application to the Coulomb Scattering 2.5.4 Fock-Schwinger Proper Time Method 3. Quantization--Free Fields 3.1 Canonical Quantization 3.1.1 General Formulation 3.1.2 Scalar Field 3.1.3 Charged Scalar Field 3.1.4 Time-Ordered Product 3.1.5 Thermodynamic Equilibrium 3.2 Quantized Radiation Field 3.2.1 Indefinite Metric 3.2.2 Propagator 3.2.3 Massive Vector Field 3.2.4 Vacuum Fluctuations 3.3 Dirac Field and Exclusion Principle 3.3.1 Anticommutators 3.3.2 Fock Space for Fermions 3.3.3 Relation between Spin and Statistics--Propagator 3.4 Discrete Symmetries 3.4.1 Parity 3.4.2 Charge Conjugation 3.4.3 Time Reversal 3.4.4 Summary 4. Interaction with an External Field 4.1 Quantized Electromagnetic Field Interacting with a Classical Source 4.1.1 Emission Probabilities 4.1.2 Emitted Energy and the Infrared Catastrophe 4.1.3 Induced Absorption and Emission 4.1.4 S Matrix and Evolution Operator 4.2 Wick's Theorem 4.2.1 Bose Fields 4.2.2 Fermi Fields 4.2.3 General Case 4.3 Quantized Dirac Field Interacting with a Classical Potential 4.3.1 General Formalism 4.3.2 Emission Rate to Lowest Order 4.3.3 Pair Creation in a Constant Uniform Electric Field 4.3.4 The Euler-Heisenberg Effective Lagrangian 5. Elementary Processes 5.1 S Matrix and Asymptotic Theory 5.1.1 Cross Sections 5.1.2 Asymptotic Theory 5.1.3 Reduction Formulas 5.1.4 Generating Functional 5.1.5 Connected Parts 5.1.6 Fermions 5.1.7 Photons 5.2 Applications 5.2.1 Compton Effect 5.2.2 Pair Annihilation 5.2.3 Positronium Lifetime 5.2.4 Bremsstrahlung 5.3 Unitarity and Causality 5.3.1 Unitarity and Partial Wave Decomposition 5.3.2 Causality and Analyticity 5.3.3 The Jost-Lehmann-Dyson Representation 5.3.4 Forward Dispersion Relations 5.3.5 Momentum Transfer Analyticity 6. Perturbation Theory 6.1 Interaction Representation and Feynman Rules 6.1.1 Self-Interacting Scalar Field 6.1.2 Feynman Rules for Spinor Electrodynamics 6.1.3 Electron-Electron and Electron-Positron Scattering 6.1.4 Scalar Electrodynamics 6.2 Diagrammatics 6.2.1 Loopwise Expansion 6.2.2 Truncated and Proper Diagrams 6.2.3 Parametric Representation 6.2.4 Euclidean Green Functions 6.3 Analyticity Properties 6.3.1 Landau Equations 6.3.2 Real Singularities 6.3.3 Real Singularities of Simple Diagrams 6.3.4 Physical-Region Singularities. Cutkosky Rules 7. Radiative Corrections 7.1 One-Loop Renormalization 7.1.1 Vacuum Polarization 7.1.2 Electron Propagator 7.1.3 Vertex Function 7.1.4 Summary 7.2 Radiative Corrections to the Interaction with an External Field 7.2.1 Effective Interaction and Anomalous Magnetic Moment 7.2.2 Radiative Corrections to Coulomb Scattering 7.2.3 Soft Bremsstrahlung 7.2.4 Finite Inclusive Cross Section 7.3 New Effects 7.3.1 Photon-Photon Scattering 7.3.2 Lamb Shift 7.3.3 Van der Waals Forces at Large Distances 8. Renormalization 8.1 Regularization and Power Counting 8.1.1 Introduction 8.1.2 Regularization 8.1.3 Power Counting 8.1.4 Convergence Theorem 8.2 Renormalization 8.2.1 Normalization Conditions and Structure of the Counterterms 8.2.2 Bogoliubov's Recursion Formula 8.2.3 Zimmermann's Explicit Solution 8.2.4 Renormalization in Parametric Space 8.2.5 Finite Renormalizations 8.2.6 Composite Operators 8.3 Zero-Mass Limit, Asymptotic Behavior, and Weinberg's Theorem 8.3.1 Massless Theories 8.3.2 Ultraviolet Behavior and Weinberg's Theorem 8.4 The Case of Quantum Electrodynamics 8.4.1 Formal Derivation of the Ward-Takahashi Identities 8.4.2 Pauli-Villars Regularization to All Orders 8.4.3 Renormalization 8.4.4 Two-Loop Vacuum Polarization 9. Functional Methods 9.1 Path Integrals 9.1.1 The Role of the Classical Action in Quantum Mechanics 9.1.2 Trajectories in the Bargmann-Fock Space 9.1.3 Fermion Systems 9.2 Relativistic Formulation 9.2.1 S Matrix and Green Functions in Terms of Path Integrals 9.2.2 Effective Action and Steepest-Descent Method 9.3 Constrained Systems 9.3.1 General Discussion 9.3.2 The Electromagnetic Field as an Example 9.4 Large Orders in Perturbation Theory 9.4.1 Introduction 9.4.2 Anharmonic Oscillator 10. Integral Equations and Bound-State Problems 10.1 The Dyson-Schwinger Equations 10.1.1 Field Equations 10.1.2 Renormalization 10.2 Relativistic Bound States 10.2.1 Homogeneous Bethe-Salpeter Equation 10.2.2 The Wick Rotation 10.2.3 Scalar Massless Exchange in the Ladder Approximation &n 12.3 The Effective Action at the One-Loop Order 12.3.1 General Form 12.3.2 Two-Point Function 12.3.3 Other Functions 12.3.4 One-Loop Renormalization 12.4 Renormalization 12.4.1 Slavnov-Taylor Identities 12.4.2 Identities for Proper Functions 12.4.3 Recursive Construction of the Counterterms 12.4.4 Gauge Dependence of Green Functions 12.4.5 Anomalies 12.5 Massive Gauge Fields 12.5.1 Historical Background 12.5.2 Massive Gauge Theory 12.5.3 Spontaneous Symmetry Breaking 12.5.4 Renormalization of Spontaneously Broken Gauge 12.5.5 Gauge Independence and Unitarity of the S Matrix 12.6 The Weinberg-Salam Model 12.6.1 The Model for Leptons 12.6.2 Electron-Neutrino Cross Sections 12.6.3 Higher-Order Corrections 12.6.4 Incorporation of Hadrons 13. Asymptotic Behavior 13.1 Effective Charge in Electrodynamics 13.1.1 The Gell-Mann and Low Function 13.1.2 The Callan-Symanzik Equation 13.2 Broken Scale Invariance 13.2.1 Scale and Conformal Invariance 13.2.2 Modified Ward Identities 13.2.3 Callan-Symanzik Coefficients to Lowest Order 13.3 Scale Invariance Recovered 13.3.1 Coupling Constant Flow 13.3.2 Asymptotic Freedom 13.3.3 Mass Corrections 13.4 Deep Inelastic Lepton-Hadron Scattering and Electron-Positron Annihilation into Hadrons 13.4.1 Electroproduction 13.4.2 Light-Cone Dynamics 13.4.3 Electron-Positron Annihilation 13.5 Operator Product Expansions 13.5.1 Short-Distance Expansion 13.5.2 Dominant and Subdominant Operators, Operator Mixing, and Conservation Laws 13.5.3 Light-Cone Expansion Appendix A-1 Metric A-2 Dirac Matrices and Spinors A-3 Normalization of States, S Matrix, Unitarity, and Cross Sections A-4 Feynman Rules Index

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Relativistic Cosmology - 2826696358

947,57 zł

Relativistic Cosmology Cambridge University Press

Książki / Literatura obcojęzyczna

Cosmology has been transformed by dramatic progress in high-precision observations and theoretical modelling. This book surveys key developments and open issues for graduate students and researchers. Using a relativistic geometric approach, it focuses on the general concepts and relations that underpin the standard model of the Universe. Part I covers foundations of relativistic cosmology whilst Part II develops the dynamical and observational relations for all models of the Universe based on general relativity. Part III focuses on the standard model of cosmology, including inflation, dark matter, dark energy, perturbation theory, the cosmic microwave background, structure formation and gravitational lensing. It also examines modified gravity and inhomogeneity as possible alternatives to dark energy. Anisotropic and inhomogeneous models are described in Part IV, and Part V reviews deeper issues, such as quantum cosmology, the start of the universe and the multiverse proposal. Colour versions of some figures are available at www.cambridge.org/9780521381154.

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The Quantum Theory of Fields - 2826693875

580,04 zł

The Quantum Theory of Fields Cambridge University Press

Książki / Literatura obcojęzyczna

Available for the first time in paperback, The Quantum Theory of Fields is a self-contained, comprehensive, and up-to-date introduction to quantum field theory from Nobel Laureate Steven Weinberg. Volume II gives an up-to-date and self-contained account of the methods of quantum field theory, and how they have led to an understanding of the weak, strong, and electromagnetic interactions of the elementary particles. The presentation of modern mathematical methods is throughout interwoven with accounts of the problems of elementary particle physics and condensed matter physics to which they have been applied. Many topics are included that are not usually found in books on quantum field theory. The book contains much original material, and is peppered with examples and insights from the author's experience as a leader of elementary particle physics. Exercises are included at the end of each chapter.

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Quantum Mechanics - 2843293794

446,83 zł

Quantum Mechanics Nova Science Publishers Inc

Książki / Literatura obcojęzyczna

The book Quantum Mechanics: Principles, New Perspectives, Extensions and Interpretation Revised Edition deals with the foundations of Quantum Mechanics in a quite novel way. From his own published works throughout these last 20 years in prominent Journals, Prof. L.S.F. Olavo reconstructs Quantum Mechanics (as related to the Schrdinger equation) from the scratch, both in mathematical and interpretive ways. The picture that emerges is quite different from the one we get from other approaches. While the mainstream approach reinforces some unavoidable weirdness in the Quantum World, Prof. Olavos interpretation presents Quantum Mechanics as quite an intuitive theory, using only the pedestrian notions of randomness, fluctuations and the companion notion of statistics. However, it is much more than another stochastic approach. Throughout the first part of the book, Prof. Olavo shows how the various roads to derive the Schrdinger equation can be reduced to his own mathematical construction: Feynmans path integral and the stochastic approach are but two of them. The book also brings about quite new results, such as the connection between Quantum Mechanics and the Central Limit Theorem and Langevin Equations (by means of which quantum phenomena can be easily simulated and make visualizable). All this is done taking recourse to only three axioms. This strategy gives the book an impressive power of synthesis in what respects the interpretation of the formalism. In fact, in the last part of the book, Prof. Olavo shows how some of the innumerous proposals for the interpretation of Quantum Mechanics, with some of their constructs, can help us making a rational reconstruction of a Quantum World without any weirdness whatsoever. In the second part, to remove some of the various obstacles to a Quantum Mechanics without weirdness, the book deals with the most prominent aspects and experiments of the Quantum, such as spin and the Stern-Gerlach experiment, the construction of operators and also Identical Particles. In the third part, the book presents a fully special and general relativistic extension of the formalism by just making the extension of the three postulates used throughout the first part. This book is intended to all those interested in the foundations of Quantum Mechanics.

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Quantum Mechanics - 2826691517

162,19 zł

Quantum Mechanics Dover Publications

Książki / Literatura obcojęzyczna

"Strongly recommended" by the American Journal of Physics, this volume serves as a text for advanced undergraduates and graduate students of physics as well as a reference for professionals. Clear in its presentation and scrupulous in its attention to detail, the treatment originally appeared in a two-volume French edition. This convenient single-volume translation begins with formalism and its interpretation, starting with the origins of quantum theory and examinations of matter waves and the Schrödinger equation, one-dimensional quantized systems, the uncertainty relations, and the mathematical framework and physical content of formalism. The second half opens with an exploration of symmetries and invariance, including a consideration of angular momentum, identical particles and the Pauli exclusion principle, invariance and conservation laws, and time reversal. Methods of approximation include those involving stationary perturbations, the equation of motion, variational method, and collision theory. The final chapters review the elements of relativistic quantum mechanics, and each of the two volumes concludes with useful appendixes. Reprint of the John Wiley & Sons, New York, two-volume 1958 edition.

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Quantum Mechanics of One- And Two-Electron Atoms - 2836092539

106,50 zł

Quantum Mechanics of One- And Two-Electron Atoms DOVER PUBLICATIONS

Książki / Literatura obcojęzyczna

I. The hydrogen atom without external fields a) Nonrelativistic theory b) Dirac theory c) Radiative and other corrections II. The helium atom without external fields a) Nonrelativistic theory b) Relativistic theory III. Atoms in external fields a) Zeeman effect b) Stark effect in hydrogen c) Stark effect in helium IV. Interaction with radiation a) Discrete spectrum b) The photoeffect c) Bremsstrahlung Appendix on spherical harmonics Bibliography Addenda and errata Further addenda and errata Author index Subject index Index of Tables

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Charged Particle Traps II - 2853395089

846,60 zł

Charged Particle Traps II Springer, Berlin

Książki / Literatura obcojęzyczna

This is the second volume of Charged Particle Traps devoted to applications, complementing the first volume s comprehensive treatment of the theory and practice of charged particle traps, their many variants and refinements. In recent years, applications of far reaching importance have emerged ranging from the ultra-precise mass determinations of elementary particles and their antiparticles and short-lived isotopes, to high-resolution Zeeman spectroscopy on multiply-charged ions, to microwave and optical spectroscopy, some involving "forbidden" transitions from metastable states of such high resolution that optical frequency standards are realized by locking lasers to them. Further the potential application of trapped ions to quantum computing is explored, based on the extraordinary quantum state coherence made possible by the particle isolation. Consideration is given to the Paul and Penning traps as potential quantum information processors.

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