Abstract
In this lecture note 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.
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