Position, momentum, and wave spreading in curved space

Abstract

The effect of the geometry (deviation from the flat space) on the quantum evolution of the momentum and position of a free particle is discussed. It is shown that beginning with a wave-packet of minimum uncertainty (a Gaussian wave), there is a usual increase in the product of the volume uncertainties in the momentum and position space, as seen in the quantum mechanics on a flat spaces. But there is also a contribution from geometry. The leading order of this contribution is calculated.