# Statistical physics. Density matrix

## Homework Statement

A system is subject to Hamiltonian ##\hat{H}=-\gamma B_z \hat{S}_z##. Write down the density matrix.[/B]

## Homework Equations

For canonical ensemble
##\hat{\rho}=\frac{1}{Tr(e^{-\beta \hat{H}})}e^{-\beta \hat{H}}##

In general ##\rho=\sum_m |\psi_m\rangle \langle \psi_m|##

## The Attempt at a Solution

How to know which definition of density matrix to use? Thanks.

## Answers and Replies

vanhees71
Gold Member
2021 Award
The density matrix (statistical operator) is, of course, not determined by just giving the Hamiltonian but by the state of the system, because the statistical operator describes the state of the system. So there must be something missing from the problem statement or it is implied to consider a system in thermal equilibrium and to use the canonical ensemble. In the latter case it's not that difficult, if (again some information missing in the problem statement!) you know what spin your particle, i.e., ##s \in \{0,1/2,1,\ldots \}##.