# Bloch vector from taylor expansion

1. Nov 17, 2007

### cscott

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

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 $H=\hbar\omega\sigma_z$.

3. 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?

2. Nov 17, 2007

### nrqed

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.

3. Nov 17, 2007

### cscott

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

Thanks.