  We propose a quantum mechanics of extended objects that accounts for the
finite extent of a particle defined via its Compton wavelength. The Hilbert
space representation theory of such a quantum mechanics is presented and this
representation is used to demonstrate the quantization of spacetime. The
quantum mechanics of extended objects is then applied to two paradigm examples,
namely, the fuzzy (extended object) harmonic oscillator and the Yukawa
potential. In the second example, we theoretically predict the phenomenological
coupling constant of the $\omega$ meson, which mediates the short range and
repulsive nucleon force, as well as the repulsive core radius.
