  A concise derivation of a new multiplicative product of Schwartz
distributions is presented. The new product $\star$ is defined in the vector
space ${\cal A}$ of piecewise smooth functions on $\bkR$ and all their
(distributional) derivatives; it is associative, satisfies the Leibnitz rule
and reproduces the usual product of functions for regular distributions. The
algebra $({\cal A},+,\star)$ yields a sufficiently general setting to address
some interesting problems. As an application we consider the problem of
deriving a global formulation for quantum confined systems.
