MathematicalPhysicist
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Questions 3 and 4 in the attachment.
3. The attempt at a solution
3. [tex]\int d\omega_1 d\omega_2 /r1r2=(2\pi)^2 \int_{0}^{\pi} d\theta_1 \int_{0}^{\pi} d\theta_2 \frac{1}{\sqrt{r_1^2+r_2^22r_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((xx_A+xx_B)/a)dx[/tex]
Now I can assume that x_A is at the origin and x_B=Rx, where R is the seperation between the two atoms, i.e the exponenet becomes: [tex]exp((x+\sqrt{x^2+R^22Rxcos(\theta))[/tex], but still how do I proceed from here?
Thanks in advance.
here's the attachment in case the link doesn't show.
3. The attempt at a solution
3. [tex]\int d\omega_1 d\omega_2 /r1r2=(2\pi)^2 \int_{0}^{\pi} d\theta_1 \int_{0}^{\pi} d\theta_2 \frac{1}{\sqrt{r_1^2+r_2^22r_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((xx_A+xx_B)/a)dx[/tex]
Now I can assume that x_A is at the origin and x_B=Rx, where R is the seperation between the two atoms, i.e the exponenet becomes: [tex]exp((x+\sqrt{x^2+R^22Rxcos(\theta))[/tex], but still how do I proceed from here?
Thanks in advance.
here's the attachment in case the link doesn't show.
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