- #1
stumpoman
- 10
- 1
Homework Statement
Show that
[tex] \left [ A,B \right ]^{\dagger}=-\left [A,B \right ] [/tex]
Homework Equations
[tex] \left [ A,B \right ] = AB-BA [/tex][tex] \left (AB \right)^{\dagger}= B^{\dagger}A^{\dagger} [/tex]
The Attempt at a Solution
[tex] \left [ A,B \right ]^{\dagger}=\left (AB-BA \right )^{\dagger} [/tex][tex]=\left (AB \right )^{\dagger}-\left (BA \right )^{\dagger} [/tex][tex]=B^{\dagger}A^{\dagger}-A^{\dagger}B^{\dagger}[/tex][tex]=-\left (A^{\dagger}B^{\dagger}-B^{\dagger}A^{\dagger} \right )[/tex][tex]=-\left [ A^{\dagger},B^{\dagger} \right ][/tex]
I can only see this working if the operators are Hermitian but the question did not specify it as such.