What Is the Density Operator of an Unknown System?

[sunrah]

Homework Statement

What is the density operator (statistical operator) of a system about which nothing is known?

Homework Equations

$\hat{\rho} = \sum p_{i} |i\rangle\langle i|$

The Attempt at a Solution

If nothing is known about a system we must assume something in order to make worthwhile statements about it. So if no one state can be preferred over another then it seems a normal distribution of states is likely. This means for N states the $p_{i} = \frac{1}{N}$

Putting this in the general definition of density operator gives

$\hat{\rho} = \frac{1}{N} \sum |i\rangle\langle i| = \frac{1}{N}\cdot \hat{1}$

Really?

 

[dextercioby]

Looks good to me.