- #1

- 169

- 0

## Homework Statement

a.) Show [itex] \hat {(Q^\dagger)}^\dagger=\hat Q [/itex], where [itex] \hat {Q^\dagger} [/itex] is defined by [itex] <\alpha| \hat Q \beta>= <\hat Q^ \dagger \alpha|\beta> [/itex].

b.) For [itex] \hat Q =c_1 \hat A + c_2 \hat B [/itex], show its Hermitian conjugate is [itex] \hat Q^\dagger =c_1^* \hat A^\dagger + c_2^* \hat B^\dagger [/itex].

## Homework Equations

a.) I found an example that might be related to this problem. It says that [itex] |T^\dagger \alpha> = T^\dagger |\alpha> [/itex] and [itex] <T|=(|T>)^\dagger [/itex] .

## The Attempt at a Solution

For part (a), I'm thinking that I might be rewrite the right hand side of the second equation. From the relevant equations I gave, do you think [itex] <\hat Q^\dagger \alpha| \beta> = \hat Q^\dagger <\alpha| \beta> [/itex] is permitted? And if so, how do I proceed from here?