Maxime Clusel Marc Magr Angel Alastuey

PHYSICS AND MATHEMATICAL TOOLS

• Gebundenes Buch

Produktbeschreibung

This book presents mathematical methods and tools which are useful for physicists and engineers: response functions, Kramers-Kronig relations, Green's functions, saddle point approximation. The derivations emphasize the underlying physical arguments and interpretations without any loss of rigor. General introductions describe the main features of the methods, while connections and analogies between a priori different problems are discussed. They are completed by detailed applications in many topics including electromagnetism, hydrodynamics, statistical physics, quantum mechanics, etc. Exercises are also proposed, and their solutions are sketched. A self-contained reading of the book is favored by avoiding too technical derivations, and by providing a short presentation of important tools in the appendices. It is addressed to undergraduate and graduate students in physics, but it can also be used by teachers, researchers and engineers.

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Produktdetails

• Verlag: World Scientific
• Seitenzahl: 358
• Erscheinungstermin: 30. Dezember 2015
• Englisch
• Abmessung: 250mm x 175mm x 24mm
• Gewicht: 799g
• ISBN-13: 9789814713238
• ISBN-10: 9814713236
• Artikelnr.: 43718000

Inhaltsangabe

Analyticity and Linear Response: Definition of the Susceptibility
Analyticity of the Susceptibility
Kramers-Kronig Relations
Applications and Examples: Admittance of a RLC Circuit
Absorption and Dispersion in a Dielectric
Oscillating Flow in a Capillary
Response of a Plasma within the Vlasov Approximation
Conductivity and Kubo Formula
Static Green's Functions: Definition and Properties of Green's Functions
Operator Point of View
Laplace Operator
Helmholtz Operator
Applications and Examples: Origin of the Method of Images
Ball in Uniform Motion in a Fluid
Density of States of a Quantum Particle
Scattering by a Repulsive Potential
Time-Dependent Green's Functions: Green's Functions and Causality
Diffusion Equation
Schrödinger Equation
Wave Equation
Applications and Examples: Diffusion on a Segment
Fraunhofer Diffraction
Emission of Sound Waves
Wavefront in Supersonic Regime
Propagation of Heat
Polarizability of the Hydrogen Atom
Saddle Point Method: Simple Integrals
Integral on a Path in the Complex Plane
Case of Multiple Integral
Applications and Examples: Equivalence of Canonical and Micro-Canonical Ensembles
Harmonic Crystal at Low Temperature
Ising Model
Semi-Classical Approximation