- #1
Calcifur
- 24
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Homework Statement
The hermitian conjugate of an operator, [itex]\hat{F}[/itex], written [itex]\hat{F}[/itex][itex]^{\tau}[/itex] satisfies the condition:
∫∅*(r)[itex]\hat{F}[/itex][itex]^{\tau}[/itex]ψ(r)dr=(∫ψ*(r)[itex]\hat{F}[/itex]∅(r)dr)*
for any choice of wavefunctions ψ and ∅. Show that:
([itex]\hat{F}[/itex]+i[itex]\hat{G}[/itex])[itex]^{\tau}[/itex]=[itex]\hat{F}[/itex][itex]^{\tau}[/itex] -i[itex]\hat{G}[/itex][itex]^{\tau}[/itex]
(10 marks)
2. The attempt at a solution
I feel like I'm missing something here, either that or the question's stupidly easily and isn't worth ten marks.
As ((A + B)* = A* + B*) and as with all complex conjugates (x+iy)*=(x-iy), it can be applied to the above as it's still just a complex conjugate. I know I'm supposed to use the condition above somehow so without obviously telling me the answer, could someone point me in the right direction for how I'm supposed to SHOW it please.
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