- #1
latentcorpse
- 1,444
- 0
I just can't see what's going wrong here
[itex]\nabla^2 p . (x-y) = p^2[/itex] where [itex]p,x,y[/itex] are all 4 vectors.
so it's obvious from looking at it but i decided to try and show it
[itex]\partial_i \partial_i (p_j r_j)[/itex] where i used r to denote x-y
[itex]= \partial_i \left( \left( \partial_i p_j \right) r_j + p_j \delta_{ij} \right)[/itex]
[itex]= \partial_i \left( \left( \partial_i p_j \right) r_j + p_i \right)[/itex]
[itex]= \left( \partial_i \partial_i p_j \right) r_j + \partial_i p_j \delta_{ij} + p_i[/itex]
[itex]= \left( \partial_i \partial_i p_j \right) r_j + \partial_i p_i + p_i[/itex]
what on Earth has gone wrong? i think I've just done to much maths today!
[itex]\nabla^2 p . (x-y) = p^2[/itex] where [itex]p,x,y[/itex] are all 4 vectors.
so it's obvious from looking at it but i decided to try and show it
[itex]\partial_i \partial_i (p_j r_j)[/itex] where i used r to denote x-y
[itex]= \partial_i \left( \left( \partial_i p_j \right) r_j + p_j \delta_{ij} \right)[/itex]
[itex]= \partial_i \left( \left( \partial_i p_j \right) r_j + p_i \right)[/itex]
[itex]= \left( \partial_i \partial_i p_j \right) r_j + \partial_i p_j \delta_{ij} + p_i[/itex]
[itex]= \left( \partial_i \partial_i p_j \right) r_j + \partial_i p_i + p_i[/itex]
what on Earth has gone wrong? i think I've just done to much maths today!