Feynman path integrals and quantum mechanics as ℏ↑0

When the space of paths is a certain Hilbert space H, we show how to extend the Feynman path integral J of DeWitt and Albeverio and Hoegh-Krohn. Our extension enables us to integrate a wider class of functional on H. We establish a new representation for the wavefunction in nonrelativistic quantum mechanics-the quasiclassical representation. Using our extension of J and the quasiclassical representation, we discuss the problem of obtaining classical mechanics as the limiting case of quantum mechanics when ??0. Copyright © 1976 American Institute of Physics.