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Physique mathématique --- Théorie quantique --- Application des groupes a la physique --- Dirac, equation de --- Application des groupes a la physique --- Dirac, equation de

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Quantum theory. --- Schrödinger operator --- Topology. --- Dirac equation. --- Théorie quantique --- Opérateur de Schrödinger --- Topologie --- Dirac, Equation de --- Schrödinger operator. --- Schrödinger, Opérateur de --- Dirac, équation de --- Schrödinger operator --- Théorie quantique --- Opérateur de Schrödinger --- Théorie quantique. --- Schrödinger, Opérateur de. --- Topologie. --- Dirac, Équation de.

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Kerr black holes --- Black holes (Astronomy) --- Inverse scattering transform. --- Dirac equation. --- Kerr, Trous noirs de --- Trous noirs (Astronomie) --- Inverse scattering transform --- Dirac, Equation de --- Dirac equation --- kerr, Effet --- Trous noirs (astronomie) --- Problème inverse de diffusion --- Kerr, Effet. --- Dirac, Équation de. --- Problème inverse de diffusion.

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Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc., as self-adjoint operators in appropriate Hilbert spaces and their spectral analysis.  Though a naïve   treatment exists for dealing with such problems, it is based on finite-dimensional algebra or even infinite-dimensional algebra with bounded operators, resulting in paradoxes and inaccuracies.   A proper treatment of these problems requires invoking certain nontrivial notions and theorems from functional analysis concerning the theory of unbounded self-adjoint operators and the theory of self-adjoint extensions of symmetric operators. Self-adjoint Extensions in Quantum Mechanics begins by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the naïve treatment.  The necessary mathematical background is then built by developing the theory of self-adjoint extensions.  Through examination of  various quantum-mechanical systems, the authors show how quantization problems associated with the correct definition of observables and their spectral analysis can be treated consistently for comparatively simple quantum-mechanical systems.  Systems that are examined include free particles on an interval, particles in a number of potential fields including delta-like potentials, the one-dimensional Calogero problem, the Aharonov-Bohm problem, and the relativistic Coulomb problem. This well-organized text is most suitable for graduate students and postgraduates interested in deepening their understanding of mathematical problems in quantum mechanics beyond the scope of those treated in standard textbooks.  The book may also serve as a useful resource for mathematicians and researchers in mathematical and theoretical physics.

Operator theory --- Quantum mechanics. Quantumfield theory --- Mathematical physics --- Mathematics --- toegepaste wiskunde --- wiskunde --- quantumfysica --- Quantum theory --- Schrödinger equation --- Dirac equation --- Théorie quantique --- Schrödinger, Equation de --- Dirac, Equation de --- Mathématiques --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B

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Mathematical physics --- Quantum electrodynamics --- Électrodynamique quantique --- Evolution equations --- Équations d'évolution --- Maxwell equations. --- Maxwell, Équations de. --- Dirac equation. --- Dirac, Équation de. --- Mathematics. --- Asymptotic theory. --- Théorie asymptotique. --- Dirac equation --- Maxwell equations --- Electrodynamics, Quantum --- QED (Physics) --- Quantum field theory --- Schwinger action principle --- Equations, Maxwell --- Differential equations, Partial --- Electromagnetic theory --- Asymptotic theory in evolution equations --- Asymptotic expansions --- Wave equation --- Asymptotic theory --- Mathematics --- Électrodynamique quantique. --- Théorie asymptotique