Suppose we have a system with total angular momentum 1. Pick a basis corresponding to the three eigenvectors of the z-component of angular momentum, Jz, with eigenvalues +1,0,−1, respectively. We are given an ensemble described by density matrix:
ρ=41211110101.
(a) Is ρ a permissible density matrix? Give your reasoning. For the remainder of this problem, assume that it is permissible. Does it describe a pure or mixed state? Give your reasoning.
(b) Given the ensemble described by ρ, what is the average value of Jz?
(c) What is the spread (standard deviation) in measured values of Jz?