Is the Hermite Conjugate Needed for Expectation Values of Spin?

[Niles]

Homework Statement

Hi all.

The expectation value for S_x (spin in x-direction) is:

$$\left\langle {S_x } \right\rangle = \left\langle {\phi |S_x \phi } \right\rangle = \phi ^\dag S_x \phi$$
where \phi is the state and \phi^"sword" is the hermite conjugate.

My question is: I thought that when finding expectation values, you are supposed to complex conjugate the left part of the inner product, not hermite conjugate?

 

[kreil]

I am fairly certain that by definition,

$$(S^T)^*=S^{\dag}$$

so in a way it's the same thing (T is the transpose matrix)

 

[Niles]

I get it - thanks :-)