Elements of Green's Functions and Propagation: Potentials, Diffusion, and WavesThis text takes the student with a background in undergraduate 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 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 the problem. The book is based on the author's extensive teaching experience. |
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Inhalt
Readers guide | 3 |
Appendices | 4 |
Problems | 28 |
A preview | 70 |
ངང8ཚ8 ཌྲ | 92 |
II Dirichlet problems | 117 |
III Neumann problems | 142 |
IV Some points of principle | 157 |
A Notations and formulary | 371 |
spherical polar coordinates | 378 |
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 | 290 |
The Helmholtz equation | 329 |
K Sound waves | 432 |
the initial conditions on K3 verified | 439 |
relativistic methods for | 449 |
459 | |
Häufige Begriffe und Wortgruppen
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