Find density matrice at zero and infinity temperature

[romeo31415]

Homework Statement

Homework Equations

https://www.physicsforums.com/attachments/upload_2015-1-15_18-57-56-png.77691/ [Broken]
Density matrix for a 2 state system is:
https://www.physicsforums.com/attachments/upload_2015-1-15_19-1-30-png.77694/ [Broken]

The Attempt at a Solution

For a 2 finite state system, the matrice density at limit temperature is
https://www.physicsforums.com/attachments/upload_2015-1-15_18-59-39-png.77692/ [Broken]
https://www.physicsforums.com/attachments/upload_2015-1-15_18-59-56-png.77693/ [Broken] [/B]

The Attempt at a Solution

 

[DrClaude]

You wrote the density matrix in terms of the energy and $\beta$. What does the finite temperature density matrix in the problems tell you about $E_1$ and $E_2$?

Could you give some details about how you reached the solutions you wrote?

 

[romeo31415]

Homework Equations

Density matrix for a 2 state system is:

The Attempt at a Solution

For a 2 finite state system, the matrice density at limit temperature is

[/B]
Evolution of the density matrix