where i’ve let ħ, c =1
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Problem 5-3b Hint. where I’ve let ħ, c =1. †. †. . i. Recalling that is a function of k ,. it should be primed when k is. Again, I’ve adopted the ħ , c = 1. You should be able to rewrite the left-hand side of in the form:. - PowerPoint PPT PresentationTRANSCRIPT
)(2
1 2 r
L
tik
tik
rki ededekd
r
2)2()(
3
3
where I’ve let ħ,c=1.
†
Recalling that is a function of k, 22mkk
it should be primed when k is. Again, I’ve adopted the ħ,c = 1.
tik
tik
rki ededekd
ir
2)2()(
3
3†
i
)()(),( 3 rrirr You should be able to rewrite the left-hand side of in the form:
)(3
3
3
3
2)2(2)2(, rkrkie
kdkdirr
You will need to take the Fourier transform of both sides:
)(2)2(2)2(
3
3
3
3
3
rreekdkd
i rkirki
d3reiK·r eik·r d3reiK·r
I’ve already cancelled1/(2)3 from both sides
Integrating over d3r introduces a delta function that simplifies the integration over d3k
Next do yet ANOTHER Fourier transform:
)(2
333
rrerdekd
i riri
KK d3r'eiK'·r' eik·r d3r'eiK'·r'
Again already canceling1/(2)3 from both sides
Problem 5-3b Hint
You should be able to take it from here, completing the arguments to show
)(, 3 kk dd kk
†