Elements of Green's Functions and Propagation: Potentials, Diffusion, and Waves

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Clarendon Press, 1989 - Science - 465 pages
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This 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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Contents

Introduction i
2
Diffusion m
3
Appendices
4
Ordinary differential equations
41
A preview
70
Potentials
89
II Dirichlet problems
117
III Neumann problems
142
III Examples
290
The Helmholtz equation
329
A Notations and formulary
371
B The Dirichlet integral
384
E Degeneracy and reality properties of complex
397
Dilemmas with notations for boundary and initial
410
Greens functions for circle
412
the variational method and
426

IV Some points of principle
157
Summary
173
II General theory
201
Summary
229
II Unbounded space
262
K Sound waves
432
the initial conditions on K verified
439
relativistic methods for
449
Index
459
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About the author (1989)

G. Barton is at University of Sussex.

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