About some properties of the canonical density matrix versus the canonical Bloch equation

We examine some properties of the non-normalized (or canonical) density matrix in the coherent states representation, by two equivalent ways. On the one hand by its definition, and on the other hand as a solution to Bloch’s canonical equation. It is concluded that, since in many cases Bloch’s differential equation is difficult to solve, in applications it is preferable to use the expression obtained directly from the definition of the canonical density matrix in the coherent states representation. This conclusion is verified by examining several cases of quantum systems with linear or quadratic energy spectrum.