On the nature of continuous physical quantities in classical and quantum mechanics

Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, thought, to desc ribe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller, have thought that the answer to this question is No--that the status of individual continuous quantities is ver y different in quantum mechanics than in classical mechanics. On the contra ry, I shall show that the same subtle issues arise with respect to continuo us quantities in classical quantum mechanics; and that it is , after all, p ossible to describe a particle as possessing a sharp position value without altering the standard formalism of quantum mechanics.