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

Hi, I am trying to show that ([tex] \lambda \hat{1})^{t} = \lambda^* \hat{1} [/tex]

where [tex] \lambda \in [/tex] C (complex numbers)

and [tex] \hat{1} [/tex] is the identity operator.

3. The attempt at a solution

[tex]\int \Psi^* (\lambda \hat{1} )^{t} \Psi d^{3} {r} = \int (\lambda \hat{1} \Psi)^* \Psi d^{3} {r}[/tex]

= [tex]\lambda^*\int (\hat{1}\Psi)^* \Psi d^{3} {r} [/tex]

= [tex]\int \Psi^* \lambda^*\hat{1}^{t} \Psi d^{3} {r} [/tex]

finally, since [tex]\hat{1}[/tex] is hermitian, [tex]\hat{1}^{t}[/tex] = [tex]\hat{1}[/tex]

so

[tex]\int \Psi^* (\lambda\hat{1})^{t} \Psi d^{3} {r}[/tex] = [tex]\int \Psi^* \lambda^*\hat{1} \Psi d^{3} {r}[/tex]

Am I correct? (please excuse my multiple re-edits, I am learning the notation on the fly)

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# Homework Help: Adjunct operator proof (simple!) please tell me if I am right.

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