  Motived by the necessity of explicit and reliable calculations, as a valid
contribution to clarify the effectiveness and, possibly, the limits of the
Tsallis thermostatistics, we formulate the Two-Time Green Functions Method in
nonextensive quantum statistical mechanics within the optimal Lagrange
multiplier framework, focusing on the basic ingredients of the related Spectral
Density Method. Besides, to show how the SDM works we have performed, to the
lowest order of approximation, explicit calculations of the low-temperature
properties for a quantum $d$-dimensional spin-1/2 Heisenberg ferromagnet with
long-range interactions decaying as $1/r^{p}$ ($r$ is the distance between
spins in the lattice)
