We derive continuity equation and exact expression for flow probability density in a space with arbitrary deformed algebra leading to the minimal length. In coordinate representation the flow probability density is presented as infinite series over parameter of deformation which in momentum representation can be casted into exact closed form determined by deformed kinetic energy. The flow probability density is calculated explicitly for plane wave and for superposition of two plane waves. The results are also applied to tunnelling problem through potential barrier in a space with deformed algebra.

中文翻译：

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最小长度空间中的精确连续性方程

我们推导了具有任意变形代数并导致最小长度的空间中流动概率密度的连续性方程和精确表达式。在坐标表示中，流动概率密度表示为变形参数上的无穷级数，在动量表示中可以将其转换为由变形动能确定的精确闭合形式。对于平面波和两个平面波的叠加，显式计算出流动概率密度。该结果还适用于代数空间中通过势垒的隧穿问题。