Although the equilibrium theory of classical fluids, simple and comple
x, has reached the stage of routine accurate evaluation, this is hardl
y the case for even the next microscopic step, that of a quantum parti
cle in a classical fluid. In many chemical applications, the quantum p
article is an electron, but positron annihilation experiments on therm
alized positrons and orthopositronium atoms offer a wealth of informat
ion to test our theoretical understanding of this general class of sys
tems. Here, we investigate several ways in which the concepts behind c
lassical techniques can be generalized to handle this prototypical qua
ntum problem, in the overt quantum form as well as in the classical po
lymer representation. Both integral equation and density functional fo
rmats are studied and their qualitative characteristics examined.