- #1
vizart
- 18
- 0
I am having bit of a problem proving Eq. (0.2):
[tex](0.1) \text{ } G_{\omega}(t-t^\prime)=\theta(t-t^\prime) \frac{e^{-i\omega(t-t^\prime)}}{2\omega}+\theta(t^\prime-t) \frac{e^{i\omega(t-t^\prime)}}{2\omega}[/tex]
[tex] (0.2) \text { }\left (-\partial^2_{t}-\omega^2 \right ) G_\omega (t-t^\prime)=i\delta(t-t^\prime)[/tex]
The problem is dealing with the first and second order derivatives of the theta function in Eq. (0.1); they don't match the right hand side of (0.2).
MODs: It's not a homework problem.
[tex](0.1) \text{ } G_{\omega}(t-t^\prime)=\theta(t-t^\prime) \frac{e^{-i\omega(t-t^\prime)}}{2\omega}+\theta(t^\prime-t) \frac{e^{i\omega(t-t^\prime)}}{2\omega}[/tex]
[tex] (0.2) \text { }\left (-\partial^2_{t}-\omega^2 \right ) G_\omega (t-t^\prime)=i\delta(t-t^\prime)[/tex]
The problem is dealing with the first and second order derivatives of the theta function in Eq. (0.1); they don't match the right hand side of (0.2).
MODs: It's not a homework problem.