Is This Equation for Expectation Values Correct?

[Niles]

Homework Statement

Hi

Say I have the following number:

<br /> \left\langle {\psi _i |A|\psi _j } \right\rangle<br />

1) First of all, am I correct when saying that

<br /> \left\langle {\psi _i |A|\psi _j } \right\rangle = \left\langle {\psi _j |A^\dag |\psi _i } \right\rangle ^* <br />

where the asterix denotes complex conjugation and the dagger means Hermitian conjugate?

2) Since what we are dealing with above is just scalars, then I am correct when I say the following is true, right?

<br /> \left\langle {\psi _j |A^\dag |\psi _i } \right\rangle \left\langle {\psi _i |A|\psi _j } \right\rangle = \left\langle {\psi _i |A|\psi _j } \right\rangle \left\langle {\psi _j |A^\dag |\psi _i } \right\rangle <br />


Niles.

 

[vela]

Yup.

 

[Niles]

Thanks,