- #1
latentcorpse
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This may well be the wrong place to post this so apologies for that if it's the case.
Anyway, I'm stuck on this question, any help appreciated
Use Gauss' Theorem to show that:
(i) If [itex] \psi($\mathbf{r}$) ~ \frac{1}{r} [/itex] as [itex] r \rightarrow \infty [/itex],
then,
[itex] \int_V {\psi \nabla^{2} \psi} dV \less 0 [/itex] where the integral is over all space.
Hint: take [itex] \mathbf{V}=\psi \nabla \psi [/itex]
My initial plan of attack was to write the integral as
[itex] \int_V {\nabla \cdot \mathbf{V}} dV [/itex]
which then becomes using the divergence theorem
[itex] \oint_S {\mathbf{V} \cdot \mathbf{n}} dS [/itex]
This probably isn't right because I then have no clue how to show this is less than 0
Anyway, I'm stuck on this question, any help appreciated
Use Gauss' Theorem to show that:
(i) If [itex] \psi($\mathbf{r}$) ~ \frac{1}{r} [/itex] as [itex] r \rightarrow \infty [/itex],
then,
[itex] \int_V {\psi \nabla^{2} \psi} dV \less 0 [/itex] where the integral is over all space.
Hint: take [itex] \mathbf{V}=\psi \nabla \psi [/itex]
My initial plan of attack was to write the integral as
[itex] \int_V {\nabla \cdot \mathbf{V}} dV [/itex]
which then becomes using the divergence theorem
[itex] \oint_S {\mathbf{V} \cdot \mathbf{n}} dS [/itex]
This probably isn't right because I then have no clue how to show this is less than 0