- #1
atomicpedals
- 209
- 7
Homework Statement
Show that [itex]\left\langle[/itex]x|p|x'[itex]\right\rangle[/itex] = [itex]\hbar[/itex]/i [itex]\partial[/itex]/[itex]\partial[/itex]x [itex]\delta[/itex](x-x')
2. The attempt at a solution
[itex]\left\langle[/itex]x|p|x'[itex]\right\rangle[/itex] = i[itex]\hbar[/itex] [itex]\delta[/itex](x-x')/(x-x') = i[itex]\hbar[/itex] [itex]\partial[/itex]/[itex]\partial[/itex]x' [itex]\delta[/itex](x-x') = [itex]\hbar[/itex]/i [itex]\partial[/itex]/[itex]\partial[/itex]x [itex]\delta[/itex](x-x')
For the sake of formality I think I need an integral after my first equals sign which I think would be:
[itex]\int[/itex][itex]\delta[/itex](x-x') p [itex]\delta[/itex](x-x') dx'= p[itex]\int[/itex][itex]\delta[/itex](x-x') p [itex]\delta[/itex](x-x') dx'
However I'm not sure if a) it's needed, or b) if I set it up correctly. Any help would be appreciated!