- #1

happyparticle

- 438

- 20

- Homework Statement
- Consider a spin i, integer or half integer with the states n = -i, -(i-1),..(i-1), i

Z component of the spin is ##S_z = n\hbar## and the energy eigenvalues of this system in a magnetic field are given by: ##E_n = nh##

Find the partition function in term of 2 sinh ratio

- Relevant Equations
- ##Z = \sum_{-i}^{i} = e^{-E_n \beta}##

##Z = \sum_{-i}^{i} = e^{-E_n \beta}##

##Z = \sum_{0}^j e^{nh\beta} + \sum_{0}^j e^{-nh\beta}##

Those sums are 2 finites geometric series

##Z = \frac{1- e^{h\beta(i+1)}}{1-e^{h\beta}} + \frac{1-e^{-h\beta(i+1)}}{1-e^{-h\beta}}##

I don't think this is ring since from that I can't get 2 sinh. However, I'm not sure where is my error.

##Z = \sum_{0}^j e^{nh\beta} + \sum_{0}^j e^{-nh\beta}##

Those sums are 2 finites geometric series

##Z = \frac{1- e^{h\beta(i+1)}}{1-e^{h\beta}} + \frac{1-e^{-h\beta(i+1)}}{1-e^{-h\beta}}##

I don't think this is ring since from that I can't get 2 sinh. However, I'm not sure where is my error.