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

1. Mar 27, 2010

### qualal

1. The problem statement, all variables and given/known data

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

where $$\lambda \in$$ C (complex numbers)

and $$\hat{1}$$ is the identity operator.

3. The attempt at a solution

$$\int \Psi^* (\lambda \hat{1} )^{t} \Psi d^{3} {r} = \int (\lambda \hat{1} \Psi)^* \Psi d^{3} {r}$$

= $$\lambda^*\int (\hat{1}\Psi)^* \Psi d^{3} {r}$$

= $$\int \Psi^* \lambda^*\hat{1}^{t} \Psi d^{3} {r}$$

finally, since $$\hat{1}$$ is hermitian, $$\hat{1}^{t}$$ = $$\hat{1}$$

so

$$\int \Psi^* (\lambda\hat{1})^{t} \Psi d^{3} {r}$$ = $$\int \Psi^* \lambda^*\hat{1} \Psi d^{3} {r}$$

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

Last edited: Mar 28, 2010