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" Topological Effects in Quantum Mechanics "
edited by G. N. Afanasiev.
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BL
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579635
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b408854
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| Main Entry
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Afanasiev, G. N.
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| Title & Author
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Topological Effects in Quantum Mechanics\ edited by G. N. Afanasiev.
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| Publication Statement
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Dordrecht :: Springer Netherlands :: Imprint: Springer,, 1999.
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| Series Statement
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Fundamental Theories of Physics ;; 107
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| ISBN
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9789401146395
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: 9789401059596
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| Contents
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1 Introduction -- 2 Vector Potentials of Static Solenoids -- 21 Cylindrical Solenoids -- 2.2 Vector Potential of the Toroidal Solenoid -- 3 Electromagnetic Properties of Static Solenoids -- 3.1 Conditions for the Existence of Static Magnetic Solenoids -- 3.2 Currents, Magnetic Dipoles and Monopoles -- 3.3 Electric Static Solenoids -- 3.4 On the Disappearance of the Magnetic Field Inside a Solenoid -- 3.5 Vector Potentials of Toroidal Solenoids with Different Asymptotic Behaviour -- 3.6 Solenoids with Non-trivial Helicity -- 3.7 Electromagnetic Field of a Cylindrical Solenoid Moving Uniformly in a Medium -- 3.8 Generalised Helmholtz Coils and All That -- 4 Interaction of Magnetisations with an External Electromagnetic Field and a Generalisation of AmpÈRe's Hypothesis -- 4.1 Introduction -- 4.2 Magnetisation, Toroidalisation, and a Generalisation of Ampère's Hypothesis -- 4.3 Interaction with an External Electromagnetic Field -- 4.4 Magnetisations and the Debye Potential Representation -- 4.5 Physical Meaning of the ? Functions -- 4.6 Transition to Point-Like Sources -- 4.7 The Interaction of Charge Densities with an External Field -- 4.8 Motion of a Toroidal Solenoid in an External Electromagnetic Field -- 4.9 On the Inversion of the Debye Parametrisation -- 4.10 Concluding Remarks -- 5 Electromagnetic Properties of Time-Dependent Solenoids -- 5.1 Cylindrical Solenoids -- 5.2 Toroidal Solenoids -- 5.3 Elementary Time-Dependent Toroidal Sources -- 5.4 Vector Solutions of the Laplace Equation -- 6 Radiationless Time-Dependent Charge-Current Sources -- 6.1 Introduction -- 6.2 On Radiationless Topologically Non-Trivial Sources of Electromagnetic Fields -- 6.3 On Current Configurations Generating a Static Electric Field -- 6.4 On Electric Vector Potentials -- 6.5 More General Radiationless Sources -- 6.6 Concluding Remarks Toroidal Radiationless Sources -- 7 Selected Topological Effects of Quantum Mechanics -- 7.1 An Elementary Exposition of the Bohm-Aharonov Effect -- 7.2 Attempts at Proving the Non-Existence of the B-A Effect -- 7.3 Scattering of Charged Particles on Two Infinite Cylindrical Solenoids -- 7.4 Scattering of Charged Particles by a Toroidal Solenoid -- 7.5 On the Super-Current Arising in a Superconducting Ring -- 7.6 The Time-Dependent Bohm-Aharonov Effect -- 7.7 Scattering of Charged Particles in an Ideal Multiply Connected Spacial Region -- 7.8 On the Alternative Interpretation of the Bohm-Aharonov Effect -- 7.9 The B-A Effect for Bound States -- 7.10 Quantum Impenetrability and Bohm-Aharonov Scattering -- 7.11 The Aharonov-Casher Effect -- 8 Topological Effects for the Free Electromagnetic Field -- 8.1 Introduction -- 8.2 Relativistic Helicity and Its Physical Meaning -- 8.3 Gauge-Invariant Representation for the Energy of a Weak Gravitational Field -- 8.4 Photon Densities -- 8.5 Numerical Results -- 8.6 On the Ehrenfest-Pauli Objections -- 8.7 On the Hegerfeldt Theorem and All That -- 8.8 Electromagnetic Waves versus Photons -- 8.9 Discussion -- 9 Topology of the Vavilov-Cherenkov Radiation Field -- 9.1 Introduction -- 9.2 Mathematical Preliminaries -- 9.3 Electromagnetic Field of a Uniformly Moving Charge on Finite and Infinite Intervals -- 9.4 Vavilov-Cherenkov Effect and Accelerated Motion of a Charged Particle -- References.
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| Abstract
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Among the subjects covered in this volume are the topological effects of quantum mechanics, including Bohm-Aharonov and Aharonov-Casher effects and their generalisations; the toroidal moments, anapoles and their generalisations; the numerical investigation of Tonomura experiments testing the foundations of quantum mechanics; the time-dependent Bohm-Aharonov effect, the thorough study of toroidal solenoids and their use as effective transmitters of electromagnetic waves; and the topical questions of the Vavilov-Cherenkov radiation. Furthermore, concrete advice is given for the construction of magnetic and electric solenoids and the performance of experiments on the Bohm-Aharonov effect. In addition, properties of remarkable charge-current configurations and practical applications are studied. Audience: This volume will be of interest to postgraduate students and researchers dealing with new effective sources of electromagnetic waves.
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Physics.
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Quantum theory.
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SpringerLink (Online service)
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