LEADER 05677nam 22007695 450 001 996466801103316 005 20200629202226.0 010 $a3-319-52437-2 024 7 $a10.1007/978-3-319-52437-5 035 $a(CKB)3850000000027352 035 $a(DE-He213)978-3-319-52437-5 035 $a(MiAaPQ)EBC6304912 035 $a(MiAaPQ)EBC5590858 035 $a(Au-PeEL)EBL5590858 035 $a(OCoLC)985094719 035 $a(PPN)200509667 035 $a(EXLCZ)993850000000027352 100 $a20170427d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGreen?s Functions in Classical Physics$b[electronic resource] /$fby Tom Rother 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XI, 267 p. 45 illus., 1 illus. in color.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v938 311 $a3-319-52436-4 327 $aPrologue -- About the State of Physics -- Basic Structural Elements of Physics -- About Classical Physics and Quantum Mechanics -- Green's Functions of Classical Particles -- The Simple Harmonic Oscillator -- The Damped Harmonic Oscillator -- Elementary Motions of a Point Mass -- Lippmann-Schwinger Equation -- Two Systematic Ways to Derive Green's Functions -- Temporal Boundary Value Problem of the Harmonic Oscillator -- Two Simple Interaction Processes and Huygens' Principle -- Particle Scattering on a Rigid Sphere and Kepler Problem -- Green's Functions of Classical Fields -- Comments on the Field Concept -- The Elastic String -- Poisson Equations of Higher Dimensions -- Wave Equations of Higher Dimensions -- The Scalar Helmholtz Equation -- Scattering Problems -- Probability Experiments and Green's Functions in Classical Event Spaces -- Probability Experiments in a Two-Dimensional Event Space -- Probability Experiments in a Four-Dimensional Event Space -- Outlook or Something Like an End -- Classical Free Point Mass and Green's Function of the Diffusion Equation -- Schrödinger Equation of the Free Particle and Green's Function -- Classical Fokker-Planck Equation and Schrödinger Equation -- A Relation Between the Green's Functions of the Klein-Gordon- and Dirac Equation. 330 $aThis book presents the Green?s function formalism in a basic way and demonstrates its usefulness for applications to several well-known problems in classical physics which are usually solved not by this formalism but other approaches. The book bridges the gap between applications of the Green?s function formalism in quantum physics and classical physics. This book is written as an introduction for graduate students and researchers who want to become more familiar with the Green?s function formalism. In 1828 George Green has published an essay that was unfortunately sunken into oblivion shortly after its publication. It was rediscovered only after several years by the later Lord Kelvin. But since this time, using Green?s functions for solving partial differential equations in physics has become an important mathematical tool. While the conceptual and epistemological importance of these functions were essentially discovered and discussed in modern physics - especially in quantum field theory and quantum statistics - these aspects are rarely touched in classical physics. In doing it, this book provides an interesting and sometimes new point of view on several aspects and problems in classical physics, like the Kepler motion or the description of certain classical probability experiments in finite event spaces. A short outlook on quantum mechanical problems concludes this book. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v938 606 $aPhysics 606 $aMathematical physics 606 $aMechanics 606 $aMechanics, Applied 606 $aPlanetary science 606 $aElementary particles (Physics) 606 $aQuantum field theory 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aTheoretical and Applied Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15001 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aPlanetary Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/P22060 606 $aElementary Particles, Quantum Field Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P23029 615 0$aPhysics. 615 0$aMathematical physics. 615 0$aMechanics. 615 0$aMechanics, Applied. 615 0$aPlanetary science. 615 0$aElementary particles (Physics). 615 0$aQuantum field theory. 615 14$aMathematical Methods in Physics. 615 24$aMathematical Physics. 615 24$aTheoretical and Applied Mechanics. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aPlanetary Sciences. 615 24$aElementary Particles, Quantum Field Theory. 676 $a515.35 700 $aRother$b Tom$4aut$4http://id.loc.gov/vocabulary/relators/aut$0791878 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466801103316 996 $aGreen?s Functions in Classical Physics$92105559 997 $aUNISA