A concise derivation of a new multiplicative product of Schwartz distributions is presented. The new product ? is defined in the vector space A of piecewise smooth functions on IR and all their (distributional) derivatives; it is associative, satisfies the Leibnitz rule and reproduces the usual product of functions for regular distributions. The algebra (A,+, ?) 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.
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