  This paper suggests a new way to compute the path integral for simple quantum
mechanical systems. The new algorithm originated from previous research in
string theory. However, its essential simplicity is best illustrated in the
case of a free non relativistic particle, discussed here, and can be
appreciated by most students taking an introductory course in Quantum
Mechanics. Indeed, the emphasis is on the role played by the {\it entire family
of classical trajectories} in terms of which the path integral is computed
exactly using a functional representation of the Dirac delta-distribution. We
argue that the new algorithm leads to a deeper insight into the connection
between classical and quantum systems, especially those encountered in high
energy physics.
