- #1
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Questions 3 and 4 in the attachment.
3. [tex]\int d\omega_1 d\omega_2 /|r1-r2|=(2\pi)^2 \int_{0}^{\pi} d\theta_1 \int_{0}^{\pi} d\theta_2 \frac{1}{\sqrt{r_1^2+r_2^2-2r_1r_2cos(\theta_1+\theta_2)}[/tex]
don't know how to proceed from here?
for question 4 I got to the integral:
[tex]\int_{0}^{\infty}\int_{-1}^{1}dcos(\theta)x^2exp(-(|x-x_A|+|x-x_B|)/a)dx[/tex]
Now I can assume that x_A is at the origin and x_B=Rx, where R is the separation between the two atoms, i.e the exponenet becomes: [tex]exp(-(x+\sqrt{x^2+R^2-2Rxcos(\theta))[/tex], but still how do I proceed from here?
Thanks in advance.
here's the attachment in case the link doesn't show.
The Attempt at a Solution
3. [tex]\int d\omega_1 d\omega_2 /|r1-r2|=(2\pi)^2 \int_{0}^{\pi} d\theta_1 \int_{0}^{\pi} d\theta_2 \frac{1}{\sqrt{r_1^2+r_2^2-2r_1r_2cos(\theta_1+\theta_2)}[/tex]
don't know how to proceed from here?
for question 4 I got to the integral:
[tex]\int_{0}^{\infty}\int_{-1}^{1}dcos(\theta)x^2exp(-(|x-x_A|+|x-x_B|)/a)dx[/tex]
Now I can assume that x_A is at the origin and x_B=Rx, where R is the separation between the two atoms, i.e the exponenet becomes: [tex]exp(-(x+\sqrt{x^2+R^2-2Rxcos(\theta))[/tex], but still how do I proceed from here?
Thanks in advance.
here's the attachment in case the link doesn't show.
Attachments
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