Elements of Green's Functions and Propagation: Potentials, Diffusion, and Waves
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.
Was andere dazu sagen - Rezension schreiben
Es wurden keine Rezensionen gefunden.
Ordinary differential equations
II Dirichlet problems
dimensionality under Neumann boundary conditions
The Helmholtz equation
А Notations and formulary
spherical polar coordinates
B The Dirichlet integral
F The Greens functions G as Fourier integrals
G Dilemmas with notations for boundary and initial
Greens functions for circle
Accordingly Appendix apply appropriate approximation argument boundary called Chapter charge closed complete consider constant contrast DBCs defined definition density depends derivatives determine differential equation diffusion equation discussed eigenfunctions energy entails equally evaluate example Exercise exists expansion expression fact field finite fixed follows Fourier given Green's function harmonic Hence homogeneous independent initial instance integral limit magic rule mathematical method namely NBCs normal obeys obtain operator origin physical Poisson's equation positive potential prescribed problem Proof propagator prove quantum mechanics regarded region relations representation respect result satisfies Section simply solution solve space sphere substitution surface term theorem unique unit values vanishes variables Verify volume wave equation whence write yields zero