Elements of Green's Functions and Propagation: Potentials, Diffusion, and WavesClarendon Press, 1989 - 465 Seiten This text takes the student with a background in the standard undergraduate courses in physics and mathematics towards the skills and insights needed for graduate work in theoretical physics. The author uses Green's functions to explore the physics of potentials, diffusion and waves. These are important phenomena of classical physics in their own right, but this study of the partial differential equations describing them also prepares the student for more advanced applications in many-body physics and field theory. Calculations are carried through in enough detail for self-study, and case histories illustrate the interplay between physical insight and mathematical formalism. The aim is to develop the habit of dialogue with the equations and the craftsmanship this fosters in tackling problems. |
Inhalt
Readers guide | 3 |
Appendices | 4 |
Ordinary differential equations | 41 |
A preview | 70 |
Summary | 89 |
II Dirichlet problems | 117 |
III Neumann problems | 142 |
IV Some points of principle | 157 |
The Helmholtz equation | 329 |
A Notations and formulary | 371 |
B The Dirichlet integral | 384 |
Brownian motion | 392 |
F The Greens functions Go as Fourier integrals | 400 |
G Dilemmas with notations for boundary and initial | 410 |
Greens functions for circle | 412 |
the variational method and | 426 |
Summary | 173 |
II General theory | 201 |
Summary | 229 |
II Unbounded space | 262 |
III Examples | 291 |
K Sound waves | 432 |
the initial conditions on K³ verified | 439 |
relativistic methods for | 449 |
| 459 | |
Häufige Begriffe und Wortgruppen
Appendix argument boundary conditions consider constant DBCs defined delta-function density derivatives determine differential equation diffusion equation dipole Dirichlet eigenfunctions eigenvalue energy entails evaluate Exercise exp ikR expansion explicitly expression field point finite Fourier Fredholm alternative given Go(r grad Green's function Green's theorem harmonic harmonic functions Helmholtz equation homogeneous BCs independent infinity inhomogeneous initial conditions instance integrand Laplace equation limit linear magic rule mathematical NBCs Neumann Neumann problem normal-mode obeys physical point source Poisson's equation polar potential prescribed problem Proof propagator radius region representation result satisfies Section solution solve sphere strong definition surface integral symmetry t₁ term theorem unbounded space unique values vanishes variables velocity Verify wave equation whence yields zero ηπχ
Verweise auf dieses Buch
A Guided Tour of Mathematical Methods: For the Physical Sciences Roel Snieder Eingeschränkte Leseprobe - 2001 |