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539.141 --- Nuclear forces --- Many-body problem. --- Scattering (Physics) --- Scattering (Physics). --- 539.141 Nuclear forces

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Mathematical physics --- Quantum mechanics. Quantumfield theory --- Statistical physics

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Schrodinger operators --- Schrödinger operator --- Spectral theory (Mathematics) --- Schrödinger operator. --- Spectral theory (Mathematics). --- Quantum theory --- Théorie quantique --- Schrödinger equation. --- Schrödinger, Équation de. --- Differential equations, Partial --- Schrödinger equation. --- Équations aux dérivées partielles --- Schrödinger, Équation de --- Schrödinger, Équation de --- Differential equations, Partial. --- Schrödinger equation --- Équations aux dérivées partielles. --- Schroedinger operator --- Spectral theory(Mathematics) --- Equations aux derivees partielles --- Theorie spectrale

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The first fifteen chapters of these lectures (omitting four to six chapters each year) cover a one term course taken by a mixed group of senior undergraduate and junior graduate students specializing either in mathematics or physics. Typically, the mathematics students have some background in advanced anal­ ysis, while the physics students have had introductory quantum mechanics. To satisfy such a disparate audience, we decided to select material which is interesting from the viewpoint of modern theoretical physics, and which illustrates an interplay of ideas from various fields of mathematics such as operator theory, probability, differential equations, and differential geometry. Given our time constraint, we have often pursued mathematical content at the expense of rigor. However, wherever we have sacrificed the latter, we have tried to explain whether the result is an established fact, or, mathematically speaking, a conjecture, and in the former case, how a given argument can be made rigorous. The present book retains these features.

Quantum theory --- Linear operators --- Mathematical physics --- Quantum theory. --- Linear operators. --- Mathematical physics. --- 530 --- Linear maps --- Maps, Linear --- Operators, Linear --- Quantum mechanics. Quantumfield theory --- Differential geometry. Global analysis --- Functional analysis. --- Quantum physics. --- Functional Analysis. --- Theoretical, Mathematical and Computational Physics. --- Quantum Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics

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The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.

Functional analysis. --- Mathematical physics. --- Quantum physics. --- Functional Analysis. --- Theoretical, Mathematical and Computational Physics. --- Quantum Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics --- Quantum theory. --- Quantum theory --- Mathematics.