  In this paper we define the S-bases for the spaces of tempered distributions.
These new bases are the analogous of Hilbert bases of separable Hilbert spaces
for the continuous case (they are indexed by m-dimensional Euclidean spaces)
and enjoy properties similar to those shown by algebraic bases in the finite
dimensional case. The S-bases are one possible rigorous and extremely
manageable mathematical model for the "physical" bases used in Quantum
Mechanics.
