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.

中文翻译：

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弯曲空间中的位置、动量和波传播

讨论了几何形状（偏离平面空间）对自由粒子动量和位置的量子演化的影响。结果表明，从最小不确定性的波包（高斯波）开始，动量空间和位置空间中的体积不确定性的乘积通常会增加，如在平面空间上的量子力学中所见。但也有几何学的贡献。计算此贡献的前导顺序。