- #1
v_pino
- 169
- 0
Homework Statement
Find the hermitian conjugates, where A and B are operators.
a.) AB-BA
b.) AB+BA
c.) i(AB+BA)
d.) [itex] A^\dagger A [/itex]
Homework Equations
[itex] (AB)^\dagger =B^\dagger A^\dagger [/itex]
The Attempt at a Solution
Are they correct and can I simplify them more?
a.) [itex] (AB-BA)^\dagger = (AB)^\dagger - (BA)^\dagger= B^\dagger A^\dagger - A^\dagger B^\dagger = BA-AB = -(AB-BA) [/itex]
b.) [itex] (AB+BA)^\dagger = (AB)^\dagger + (BA)^\dagger= B^\dagger A^\dagger + A^\dagger B^\dagger = BA+AB [/itex]
c.) [itex] [i(AB+BA)]^\dagger = -i[(AB)^\dagger + (BA)^\dagger]= -i(B^\dagger A^\dagger + A^\dagger B^\dagger) = BA+AB [/itex]
d.) [itex] [A^\dagger A]^\dagger = A^\dagger (A^\dagger)^\dagger=A^\dagger A [/itex]