(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: The hermitian conjugate/adjoint -Quantum Physics

**Physics Forums | Science Articles, Homework Help, Discussion**