Quantum Mechanics of Extended Objects

Abstract

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.

RevTex, 24 pages, 1 eps and 5 ps figures, format changes

References in corpus (1)

• Minimal Length Uncertainty Relation and Ultraviolet Regularisation

Cited by in corpus (5)

• Minimal Length Uncertainty Relation and gravitational quantum well
• Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length
• Effect of Minimal lengths on Electron Magnetism
• Exactly solvable dynamical models with a minimal length uncertainty
• Comment on "Quantum mechanics of smeared particles"