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Classical Electrodynamics
Physics 6561
Homework 8. Due: In class on Tuesday, 11/4.
NOTE: original problem 3 has been moved to next set
and replaced with diﬀerent problem.
1. Dirac quantization for two particles
Problem 6.17 from Jackson on page 290.
2. Causality in Coulomb gauge
Problem 6.20 from Jackson on page 291.
3. Dispersion relations
a. Some quantity satisﬁes a modiﬁed wave equation of the form
∇
2
ψ

1
v
2
∂
2
∂t
2
ψ
+
λ
v
4
∂
4
∂t
4
ψ
= 0
,
(1)
where the parameter
λ
¿
v
2
/ω
2
for the frequencies we are considering. What will be the
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Unformatted text preview: dispersion relation ω ( ~ k ) for this system? b. What would the dispersion relation be for the wave equation of the form ∇ 2 ψ1 v 2 ∂ 2 ∂t 2 ψ + λ ( ∇ 2 ) 2 ψ = 0 . (2) c. What would the dispersion relation ω ( ~ k ) be for the case with an arbitrary function F of the Laplacian showing up in the wave equation: F ( ∇ 2 ) ψ1 v 2 ∂ 2 ∂t 2 ψ = 0 . (3)...
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This note was uploaded on 10/25/2009 for the course ECE 4300 taught by Professor Lipson/pollock during the Fall '08 term at Cornell University (Engineering School).
 Fall '08
 LIPSON/POLLOCK

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