Matrix element identity with Hermitian conjugate and complex conjugation

[Niles]

Homework Statement

Hi

Say I have the following number:

$$\left\langle {\psi _i |A|\psi _j } \right\rangle$$

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

$$\left\langle {\psi _i |A|\psi _j } \right\rangle = \left\langle {\psi _j |A^\dag |\psi _i } \right\rangle ^*$$

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?

$$\left\langle {\psi _j |A^\dag |\psi _i } \right\rangle \left\langle {\psi _i |A|\psi _j } \right\rangle = \left\langle {\psi _i |A|\psi _j } \right\rangle \left\langle {\psi _j |A^\dag |\psi _i } \right\rangle$$


Niles.

 

[vela]

Yup.

 

[Niles]

Thanks,