How to Find the Bloch Vector for a Density Matrix Using Taylor Expansion?

[cscott]

Homework Statement

I need to find the bloch vector for the density matrix $\frac{1}{N}\exp{-\frac{H}{-k_bT}}$ where the Hamiltonian is given by $H=\hbar\omega\sigma_z$.

The Attempt at a Solution

I can break the Taylor series of exp into odd and even terms because sigma z squared is the identity. I get something that looks like sine and cosine but I'm missing i for Euler's equation. How else can I group the terms?

 

[nrqed]

Homework Statement

I need to find the bloch vector for the density matrix $\frac{1}{N}\exp{-\frac{H}{-k_bT}}$ where the Hamiltonian is given by $H=\hbar\omega\sigma_z$.

The Attempt at a Solution

I can break the Taylor series of exp into odd and even terms because sigma z squared is the identity. I get something that looks like sine and cosine but I'm missing i for Euler's equation. How else can I group the terms?

I am not going to be very helpful because I know little about Bloch vectors but why do you need to get an i factor? I don't see anything else to do here than to simply expand and get the sine and cos terms.

 

[cscott]

Mmm I think you're right and now I feel stupid :P

Thanks.